Pomeranz was initially drafted by the Texas Rangers in 2007 but decided to go to college instead. He was then drafted by the Cleveland Indians in the first round of the 2010 Major League Baseball Draft. He signed with the Indians on August 16, 2010, right before the deadline; his contract, which included a $2.65 million signing bonus, was the largest bonus given to a college pitcher in the draft that year.
He was considered one of the top 50 prospects in baseball in 2011.
On December 10, 2013, Pomeranz, along with minor league pitcher Chris Jensen, was traded to the Oakland Athletics for pitcher Brett Anderson. Pomeranz began 2014 as a member of the A's bullpen, where he made 9 appearances, going 1-1 with a 1.98 ERA in 13.2 innings, before being moved to the rotation on May 9 to replace the struggling Dan Straily. Pomeranz didn't give up a run in the rotation until his 4th start, on May 25, giving Oakland three 5-inning starts of shutout ball before. He made 8 starts, going 4-3 with a 3.21 ERA, striking out 37 in 42 innings, before fracturing his non-throwing hand following a poor start against the Rangers on June 16. Brad Mills took his spot in the rotation as Pomeranz went on the disabled list. He punched a wooden chair with his right hand after giving up 8 runs in 3.2 innings.