Wheeler played baseball at Childersburg High School and Wallace State Community College. The Milwaukee Brewers selected him in the 19th round of the 2007 Major League Baseball Draft. He was added to the Brewers' 40-man roster after the 2011 season, but was waived before the 2012 season began. Claimed by the Baltimore Orioles, he played in their farm system in 2012 and 2013, before signing as a free agent with the New York Yankees before the 2014 season. After starting the season in the minor leagues, Wheeler made his MLB debut on July 3, 2014.

From Sylacauga, Alabama, Wheeler attended Childersburg High School, where he played baseball and American football. A linebacker for the football team, Wheeler was named among the best players of the state of Alabama. He received offers to play college football from several Division II schools, including Jacksonville State University, Miles College, and Livingston College. He chose instead to enroll at Wallace State Community College in Hanceville, Alabama, where he played college baseball. His teammates included Derek Holland, Craig Kimbrel, and Jake Elmore.