Jansen was signed as an undrafted free agent catcher by the Dodgers organization on November 17, 2004, and was assigned to the Rookie Class Gulf Coast Dodgers, where he played in 37 games and hit .304 before being promoted to the Ogden Raptors of the Pioneer League on August 26. He had two hits in 11 at-bats in three games for Ogden. He was back with the Gulf Coast team the following season, hitting .245 in 35 games. After the season he played for the North Shore Honu in the Hawaii Winter Baseball League, where he hit .121 in nine games.

Jansen split 2007 between the Raptors and the Class-A Great Lakes Loons of the Midwest League, hitting .207 in 73 games. After the season, he again played in Hawaii Winter Baseball, this time for the West Oahu CaneFires In 2008 with the Loons, he hit .227 and 9 home runs in 79 games. He was selected to the mid-season Midwest League All-Star game.

In 2009, he was the starting catcher for the Netherlands team in the World Baseball Classic. In the Netherlands’ upset of the favored Dominican Republic team, Jansen threw out Willy Taveras on an attempted steal of third base in the ninth inning, a key play in the game. He began 2009 with the Inland Empire 66ers of San Bernardino, but hit just .202 in 38 games. Despite that, he appeared in eight games for the Triple-A Albuquerque Isotopes, but had just five hits in 27 at-bats.

Jansen was added to the Dodgers 40-man roster on November 19, 2009. He started with Inland Empire again and allowed only five runs in 18 innings while striking out 28 batters. On May 15, 2010, he was promoted to the Double-A Chattanooga Lookouts, where he was selected to the mid-season Southern League All-Star Game. He pitched 27 innings in 22 games for the Lookouts, with a 1.67 ERA.

Jansen has represented the Netherlands at three of the four World Baseball Classic’s. In 2009, he was the starting catcher for the Netherlands team in the World Baseball Classic. In the Netherlands’ upset of the favored Dominican Republic team, Jansen threw out Willy Taveras on an attempted steal of third base in the ninth inning, a key play in the game. Jansen was a late addition to the Netherlands national baseball team for the 2013 World Baseball Classic,he had transitioned to pitching in late 2009, he was added to the roster for the semi-finals but did not appear in the game.

On July 23, 2010, Jansen was promoted to the Dodgers. He made his Major League debut in relief on July 24 against the New York Mets, where he pitched a scoreless inning, retiring all three batters he faced and striking out two. On July 25, Jansen recorded his first Major League save, when he pitched a 1-2-3 inning against the Mets.

On August 26, Jansen walked and scored a run in his first Major League plate appearance, at Miller Park in Milwaukee against Yovani Gallardo of the Brewers and collected his first major league hit on August 31, at Dodger Stadium. The hit was a single up the middle against Kyle Kendrick of the Philadelphia Phillies. Jansen recorded his first win against the Houston Astros on September 11 in Minute Maid Park. He appeared in 25 games with the Dodgers in 2010, working 27 innings with a 1–0 record and a 0.67 ERA. He also saved four games in 2010.

In 2011, Jansen became a key member of the Dodgers’ bullpen. He was 2–1 with a 2.85 ERA in 53 ⁄3 innings and saved five games. Jansen also struck out 96 batters, setting a new Major League season record with 16 ⁄3 strikeouts per nine innings.

Jansen was diagnosed in 2011 with an irregular heartbeat (specifically, atrial fibrillation), and he missed some time that season while he was placed on blood thinners to prevent clots. The problem resurfaced late in the 2012 season, and he again missed considerable time while being treated. On October 24, 2012, Jansen underwent a 3-hour catheter ablation procedure in which Dr. Koonwalee Nademanee identified abnormal tissue in his left atrium and cauterized it to stop it from generating abnormal electrical signals.

In May 2012, Jansen became the Dodgers’ closer after Javy Guerra struggled in the role. At the end of the season, after missing some time due to heart problems, Jansen was replaced as closer by Brandon League. He appeared in 65 games, compiling a 5–3 record, 2.35 ERA, 99 strikeouts and 25 saves.

Jansen began 2013 as the setup man in the bullpen but resumed the role as closer when League struggled. He was in 75 games with a 4-3 record, 1.88 ERA and 28 saves. He did not allow any runs, in three appearances in the 2013 National League Division Series (NLDS) against the Atlanta Braves but was less effective in the Championship Series (NLCS) against the Cardinals, allowing two runs in two innings.

Jansen lives with his parents in Curaçao during the offseason, and they live with him in Los Angeles when they visit him during the season. Kenley is married to a Curaçao native named Gianni Jansen – Fransisca. He has a daughter, Natalia Hannah Jansen, who was born on March 16, 2013, and two sons, Kaden Isaiah Jansen, born on August 16, 2015, and Kyrian Jeremiah Jansen, born on August 22, 2018. He throws right-handed but writes with his left hand. A local team in Curaçao, the Wildcats, have renamed themselves in honour of Jansen, and competed in the Latin American Series as Wildcats KJ74.

On February 11, 2014, Jansen avoided his first arbitration hearing by signing a $4.3 million contract with the Dodgers. Fully established as the Dodgers’ closer in 2014, Jansen worked in 68 games with a 2.76 ERA, 101 strikeouts and 44 saves. He became just the fourth Dodger pitcher in history with 40+ saves in a season, joining Éric Gagné (who did it three times), Todd Worrell and Jeff Shaw. Jansen only pitched one inning in the NLDS against the Cardinals.

Jansen relies almost exclusively on a cut fastball that mostly ranges from 90–94 miles per hour (mph). Earlier in his career, he was able to throw the pitch at 98 mph, and he exceeded 100 mph in 2014. In 2012, he used this pitch about 93% of the time. His other main pitch is a slider in the low to mid 80s. He experimented with a changeup in the 2009–2011 seasons and debuted a four-seam fastball at the end of the 2012 season. He now throws four-seamer 92-96. Jansen relies both on movement and exceptional command, throwing over 70% strikes.

On January 16, 2015, he again avoided arbitration by signing a one-year $7.425 million contract with the Dodgers. However, on February 17, he underwent surgery to remove a growth from a bone in his left foot. The recovery time kept him out of action until May. Jansen was eventually activated off the disabled list on May 15 and rejoined the Dodgers roster. Jansen struck out 23 batters in his first 14 games of the season, without giving up a single walk. This broke Jay Howell’s team records (set in the 1991 season) of 13 games without a walk to start a season and 20 strikeouts without a walk to start a season. He wound up striking out 27 before he finally walked a batter on June 30, eight shy of the major league record. He made 54 appearances for the team in 2015 with a 2.41 ERA and 36 saves. He also struck out 80 batters, while only walking 8 all season. He became the first Dodgers pitcher with five seasons of 80 or more strikeouts in relief. He appeared in three games, with two saves in the 2015 NLDS and did not allow a run in 3 ⁄3 innings. In his final year of arbitration, Jansen signed a one-year, $10.65 million, contract with the Dodgers on January 15, 2016.

On June 20, 2016, Jansen picked up his 162nd career save against the Washington Nationals, breaking the all-time franchise record held by Éric Gagné. He was also selected to the National League team for the 2016 Major League Baseball All-Star Game, his first all-star selection. On August 24, 2016, Jansen tied Jim Brewer’s franchise record for strikeouts by a reliever with the 604th of his career. In 71 games, he was 3–2 with a 1.83 ERA and 47 saves, earning him the Trevor Hoffman National League Reliever of the Year Award. Of all MLB pitchers, he held right-handed batters to the lowest batting average, .107 (in 30 or more innings). In the 2016 NLDS against the Washington Nationals, Jansen pitched in four games and worked 5 ⁄3 innings, allowing four runs and saving two games. In the 2016 NLCS against the Chicago Cubs he pitched 6 ⁄3 innings over three games, with one save, and struck out 10 while only allowing one hit.

On January 10, 2017, the Dodgers announced the re-signing of Jansen to a five-year, $80 million contract. On June 11, he recorded his 200th career save against the Cincinnati Reds.

On June 2, 2017, Jansen recorded his 36th strikeout of the season, setting an MLB season record for most strikeouts without giving up a walk. The previous record was held by St. Louis Cardinals starting pitcher Adam Wainwright, who struck out 35 batters before giving up a walk in the 2013 season. The streak eventually reached 51 strikeouts before he recorded his first walk of the season on June 25 against the Colorado Rockies. He was named to his second straight All-Star Game. Jansen pitched in 65 games for the Dodgers in 2017, with five wins, a 1.32 ERA, 109 strikeouts (with only seven walks) and 41 saves. For the second straight year, he was awarded with the Trevor Hoffman National League Reliever of the Year Award.

Jansen started the playoffs by finishing all three games of the Dodgers 2017 NLDS sweep of the Diamondbacks. He saved two of the games and did not allow an earned run in 3⁄3 innings. He pitched 4⁄3 innings over four games in the 2017 NLCS against the Cubs and did not allow a batter to reach base, while striking out eight. Jansen allowed two runs to score, including a solo homer by Marwin González in Game Two of the 2017 World Series against the Houston Astros. It was his first blown save in the post-season and snapped his MLB record of converting his first 12 post-season save opportunities. In Game Five of the series, he picked up the loss in the Dodgers 10 inning defeat. In his second inning of work, he hit Brian McCann with two outs and then after a walk, he gave up a walk-off single to Alex Bregman. Overall, he pitched 8⁄3 innings over six games, with two saves and three runs allowed as the Dodgers lost the series in seven games.

After initially saying he would not pitch in the 2017 tournament, having signing a five year $80 million contract with the Dodgers in the offseason, Jansen again joined the team when they advanced to the semi finals. Jansen appeared in the teams game against Team Puerto Rico, which including Dodgers teammate Kike Hernandez. Jansen pitched a scoreless 9th inning, striking out two, but team Netherlands lost on a walk off sacrifice fly in the 11th inning.

Jansen was bothered by an injury during spring training and was slow-played after his 2017 workload, resulting in two blown saves during a shaky April. He turned it around in May, June and July and was chosen for his third straight all-star game in 2018.

He was effective against Atlanta and Milwaukee in the postseason, not allowing a run, but again struggled in the 2018 World Series, blowing two save opportunities as he allowed game-tying home runs to Jackie Bradley Jr. in Game 3 (which went 18 innings) and Steve Pearce in Game 4 as the Dodgers lost the series to the Boston Red Sox in five games.

Jansen suffered a recurrence of his irregular heartbeat prior to a game in Denver on August 9, 2018. He was placed on the 10-day disabled list and the team reported he would likely miss a month of the season. Doctors determined the condition could be controlled with medication until the offseason, so Jansen returned to the hill just 11 days later. However, the heart medication he took, which included beta blockers, had the side effects of leaving him feeling fatigued and unemotional. He gave up four home runs in his first two outings back, blowing both save opportunities, and after he protested the effects of his medication his doctors switched him to aspirin. Jansen stayed in Los Angeles when the Dodgers returned to Denver in September because he was at high risk of a stroke if he returned to elevation. Jansen completed the season and provided scoreless relief in seven of nine postseason appearances, allowing two runs in 10.2 innings (1.69 ERA).

On November 26, 2018, Jansen underwent a 5-1/2 hour heart ablation procedure, again performed by Dr. Koonlawee Nademanee, in Los Angeles. After the procedure the doctor told Jansen that small veins near the site of his 2012 procedure had grown and were agitated by dehydration, which caused the irregular signals that occurred in Denver. Jansen dedicated himself to a healthier diet after recovering from the operation and reported to spring training 25 pounds lighter. He no longer has to take blood-thinning medication.

During the 2018 MLB Players Weekend, Jansen wore the nickname “KENLEYFORNIA” on his jersey, a portmanteau blending “Kenley” and “California” in a reference to Jansen’s entrance song, “California Love” by 2Pac and Dr. Dre.

On April 7, 2019, Jansen recorded a four-out save against the Colorado Rockies at Coors Field in Denver. On May 3 and 4, Jansen converted saves against the San Diego Padres. But on May 5, pitching for the third day in a row, Jansen walked a batter and allowed two bunt singles to load the bases with no outs. He retired the next two hitters before he gave up a walkoff grand slam to Hunter Renfroe, as the Dodgers lost 8–5.

Jansen recorded two extended saves in a series against the Mets, with a 5-out save in the first game of the series and a 4-out save in the fourth game. This was his first five-out save since June 2018 in Pittsburgh. He debuted the intentional balk in the top of the ninth against the Chicago Cubs on June 15, 2019. The intentional balk was an idea he came up with bench coach Bob Geren, in which he has a runner on second and two outs and balks the runner to third to prevent the runner from stealing signs. On September 25, in a game against the San Diego Padres, Jansen picked up his 300th career save, becoming the 30th pitcher all time and the first in Dodgers history. He pitched in 62 games, with a 5–3 record and 33 saves, but a career-high ERA of 3.71.

In the 2019 NLDS, Jansen pitched to five batters and did not allow any of them to reach base.

On July 12, 2020, Jansen reported to summer training camp for the first time after recovering from COVID-19.