Kelly played the first half of the 2009 season with Greenville and Salem as a pitcher. He was elected to the All-Star Futures Game. He finished the second half of season as a shortstop. On December 8, 2009, Kelly announced his decision to continue his career as a full-time pitcher. He had hit .222 while striking out 27 percent of the time, while he had a 6–1 record with a 1.12 ERA pitching.
On December 6, 2010, Kelly was traded along with Anthony Rizzo, Reymond Fuentes, and Eric Patterson to the San Diego Padres for three-time All-Star first baseman Gonzalez. Kelly was considered the top prospect in the Red Sox organization. Entering the 2011 season, he was ranked 22 among the Top 50 Prospects by MLB.com. The Padres invited Kelly as a non-roster player to their Major League camp for 2011 Spring Training. The top prospect in the Padres' Minor League system, Kelly opened the 2011 regular season in Double-A with the San Antonio Missions.
Kelly strained his elbow in his second start for Triple-A Tucson in April 2012. He rehabilitated for 3 1⁄2 months before starting three games for San Antonio. He was promoted to the major leagues to replace the injured Jason Marquis in San Diego's starting rotation, and he made his major league debut with San Diego on August 27, 2012. Kelly earned a win after pitching six shutout innings in a 3–0 victory over the Atlanta Braves. He also recorded his first major league hit in the game. Kelly was the 15th different starting pitcher used by the Padres in 2012, which ties a club record. On March 22, 2013, Kelly was announced that he had micro tears in his UCL. He underwent Tommy John surgery on April 2 and was placed on the team's injured reserve.