On November 12, 2010, Zeller committed to play for Indiana University, turning down offers from North Carolina and Butler. Upon his commitment he was labeled "the savior of Indiana basketball." At the time Coach Tom Crean noted, "He's the most mentally focused kid I've ever recruited ... I see a young man that has mental toughness that is not normal." Zeller was nicknamed "The Big Handsome" during his time at IU.

With the addition of Zeller to the team, the Hoosiers' record in 2011–12 improved by fifteen games over the prior season, making it the largest single turnaround in the NCAA that year. The Hoosiers earned a number four seed in the 2012 NCAA Tournament and defeated New Mexico State in the second round. After defeating VCU in the third round, the Hoosiers lost in the Sweet Sixteen to Kentucky, the eventual national champions.

Due in part to Zeller's leadership, the Indiana Hoosiers finished the 2012–13 season as the outright Big Ten champions. He finished the regular season as the conference's third highest scorer (16.8 points) and second highest rebounder (8.2), along with second in the league in shooting at 57% while only trailing teammate Victor Oladipo in the Big Ten.

At the end of his sophomore season, Zeller decided to enter the 2013 NBA draft, along with teammate Victor Oladipo.

Zeller was selected with the fourth overall pick in the 2013 NBA draft by the Charlotte Bobcats. On March 31, 2014, he scored a season-high 15 points in a win over the Washington Wizards. Five days later, he recorded his first career double-double with 12 points and 11 rebounds in a win over the Cleveland Cavaliers. On May 22, he was named to the NBA All-Rookie second team after managing to play in all 82 regular season games and all four playoff games in 2013–14.

On November 11, 2015, Zeller missed two free throws with 28 seconds left in a tie game against the New York Knicks, but came back and scored on a layup off an inbounds play with 0.6 seconds remaining to lift the Hornets over the Knicks, 95–93. He finished the game with 12 points off the bench. On February 19, 2016, he scored a career-high 23 points in a 98–95 win over the Milwaukee Bucks. On March 16, he recorded his fourth double-double of the season with 13 points and 13 rebounds in a 107–99 win over the Orlando Magic.

Despite missing the entire preseason because of a right knee injury, Zeller played in the Hornets' season opener on October 26, 2016, and was 5-of-6 from the field for 15 points in 14 minutes off the bench in a 107–96 win over the Milwaukee Bucks. Five days later, he signed a four-year, $56 million contract extension with the Hornets. On November 18, 2016, he tied his career high with 23 points in a 100–96 win over the Atlanta Hawks.

Zeller is from Washington, Indiana and the nephew of former NBA player Al Eberhard. He is the youngest brother of former North Carolina and current Milwaukee Bucks center Tyler Zeller and former Notre Dame and Phoenix Suns forward-center Luke Zeller. Despite pressures brought on by unusually high expectations, commentators have noted his humility and work ethic, along with "dry wit and prankster's mirth." In May 2017, Zeller got his bachelor's degree when graduated from Indiana University's Kelley School of Business.