Drafted by the Chicago Cubs in the 28th round of the 2010 MLB Draft from the Master's College (Santa Clarita, CA). Started 2010 with the Arizona League Cubs, throwing 30.2 innings and appearing in 11 games while posting a 3-2 record with a 7.04 ERA out of the bullpen. Before 2010 ended, he was called up to single-A short season ball with the Boise Hawks, throwing in four games with one start and posting an 0-1 record with a 6.14 ERA in 7.1 innings. In 2011, Zeller started with the Arizona League Cubs, pitching in two games and throwing 4.2 innings with a 5.79 ERA. He finished 2011 with the Boise Hawks once again, appearing in 12 games and holding a 2-0 record with a 1.95 ERA in 27.2 innings pitched. Struck out 19 and walked six. 

In 2012, Zeller started the season with the double-A Tennessee Smokies, pitching in one game and throwing a scoreless inning. He was then sent down to the high-A Daytona Cubs, where he posted an 0-1 record with a 3.66 ERA in 17 games and threw 32 innings. He was called down to the single-A Boise Hawks, posting a 1.59 ERA in two games before being sent down to the high single-A Peoria Chiefs. With the Chiefs, he appeared in 11 games, starting 10. Tallied a 3.75 ERA and a 3-4 record in 60 innings pitched.