Cecil was born in Dunkirk, which is in Calvert County, Maryland. He first started playing baseball when he was eight years old near his southern Maryland home. As he got older, his father would drive him more than 20 miles each way to White Marsh Park in Bowie, Prince George’s County where there was more competition. As a teenager, he attended DeMatha Catholic High School, also in Prince George’s County. Upon graduation from Dematha, he stayed in Prince George’s County and attended the University of Maryland. In 2006, he played collegiate summer baseball for the Orleans Cardinals of the Cape Cod Baseball League.

Cecil was called up to the Toronto Blue Jays on May 1, 2009, and made his major league debut on May 5 as the starting pitcher against the Cleveland Indians at home. In that game, Cecil pitched six innings, giving up two runs, one earned, and six hits but was credited with a no-decision in a game Toronto eventually won. His next start was May 10 against the Oakland Athletics, pitching 8 scoreless innings to earn his first Major League win. Cecil defeated the Chicago White Sox, keeping Toronto in first place, but then gave up five home runs to the Boston Red Sox on May 21, losing his first game, as Toronto went on a nine-game losing streak and dropped out of first place. Cecil was returned to AAA after losing to Boston, and then pitched solidly for the Las Vegas 51s. Continued injury problems for Blue Jays’ pitchers led to Cecil being recalled to the major leagues on June 18, and he started against the Washington Nationals on June 20, filling in for the injured Casey Janssen and Roy Halladay, pitching 7 innings while allowing 3 earned runs in a no-decision, in a game Toronto lost in 12 innings.

Originally not making the rotation for the Blue Jays, Cecil was called up early in the season and became a regular in the Jays rotation along with Ricky Romero, Shaun Marcum and Brandon Morrow. On May 3, 2010, he took a perfect game into the seventh inning against the Cleveland Indians, but walked Grady Sizemore with one out. Then, two batters later, he allowed a single to Jhonny Peralta which scored Sizemore from second to end his no-hitter and his shutout. He ended up going 8 innings, allowing one hit, 2 walks, one run, and 10 strikeouts. Despite not making the original team out of spring training he led the team in wins with 15, along with a much improved 4.22 ERA.

In January 2014, Cecil filed for salary arbitration with Toronto, but came to terms on a 1-year, $1.3 million contract on January 17. He pitched the entire season out of the bullpen, making a career-high 66 appearances. In 53⁄3 innings pitched, Cecil posted a 2–3 record with a 2.70 ERA and 76 strikeouts. He also recorded 5 saves, and gave up only 2 home runs for the entire season.

On January 15, 2016, Cecil and the Blue Jays avoided salary arbitration by agreeing to a one-year, $3.8 million contract. Cecil pitched his 38th consecutive scoreless appearance on April 4 against the Tampa Bay Rays, which tied the MLB record for consecutive scoreless appearances set by Craig Kimbrel in 2011. In 2016 he was 1–7 with a 3.93 ERA.

Cecil signed a four-year, $30.5 million contract with the St. Louis Cardinals on November 21, 2016. In 2017, he was 2–4 with a 3.88 ERA in 73 relief appearances.

Cecil was released by the Cardinals organization on July 22, 2020.