Teherán signed with the Atlanta Braves on July 3, 2007, and started his professional career in 2008, pitching for the Danville Braves. During that season he started six games and had a 1–2 record with a 6.60 ERA and 17 strikeouts in 15 innings.

Prior to the 2011 season, Teherán was the top-ranked prospect by Baseball America in the Atlanta Braves system, and fifth overall of all prospects. Teherán started the year with the Triple-A Gwinnett Braves, going 3–0 with a 1.80 ERA in his first five starts. He was the starting pitcher for the World team in the 2011 All-Star Futures Game on July 10, 2011, but gave up a home run on a 95-mph fastball to the first batter, Cleveland Indians prospect Jason Kipnis, who was leading off the bottom of the first inning for the United States.

Teherán rejoined the Atlanta Braves when rosters expanded in September. He earned his first major league win against the New York Mets on September 8. He was named a starting pitcher on Baseball America’s 2011 Minor League All Star team.

Expectations for the 21-year-old Teherán were lower in 2013 than the previous spring. He was invited to the Major League spring training once again, however, where he showed flares of stardom, posting a 1.29 ERA through four starts, spanning 14.1 innings through March 16. He did not start the regular season off strong, with a 5.08 ERA in the first month, but 2013 ended up being his breakout year. He turned things around after April, finishing the season with 14-8 record, 3.20 ERA, 170 strikeouts, and 185.2 IP. On June 5, Teherán was pitching a no-hitter against the Pittsburgh Pirates through 7.2 innings before giving up a single to pinch-hitter Brandon Inge.

Teherán signed a 6-year, $32.4 million extension with the Braves on February 14, 2014. He was the Braves’ Opening Day starter for the first time in his career, taking the loss in a 2–0 game against the Milwaukee Brewers. Teherán was selected to the 2014 MLB All-Star Game, his first All-Star Game selection. However, he was ineligible due to previously pitching the Sunday before the All-Star break. He was honored as an All-Star in a pregame ceremony. Teherán became the second Colombian to be selected an All-Star, following former Braves player Édgar Rentería. In 33 starts on the season, Teheran went 14–13 with a 2.89 ERA, a 1.08 WHIP, and 186 strikeouts in 221 innings.

Teherán throws a four seam fastball that averages 92 mph, paired with a two seam fastball at 89 mph. His slider and change up both are thrown at around 82 mph. His curveball sits in the mid-70s. Teherán also has a screwball (65 mph) that he does not use very often. Teherán has a very effective pickoff move. His 22 successful attempts in 2014 through early September was the most for any pitcher during that period.

In 2015, Teherán was once again the Braves’ Opening Day starting pitcher, winning a 2–1 game against the Miami Marlins. In 33 starts, he went 11–8 with a career-high 4.04 ERA.

Teherán’s uncle Miguel worked for the Braves as a scout. Teherán’s second cousin is Sugar Ray Marimón. They grew up together in Cartagena, and were Braves teammates in 2015.

Teherán married Yoselin Rincón in February 2016. The couple’s first child was born in August of that year.

Teherán and the Los Angeles Angels agreed to terms on a one-year contract on December 21, 2019. On July 19, 2020, Teherán disclosed that he had tested positive for COVID-19. Teherán made his Angels debut on August 5, 2020 against the Seattle Mariners. While under a 60 pitch limit, he threw 2 ⁄3 innings, striking out two while allowing two runs.