[3] In his freshman year of high school, Zeller averaged 2.5 points and 1.4 rebounds per game as his team, the Washington Hatchets, won a Class 3A IHSAA state championship.

In his junior season, Zeller led Washington to a Class 3A state championship, averaging 20.5 points and 11.4 rebounds per game.

He played AAU basketball for the Indiana Elite program and led the USA 2011 squad to the Adidas Nations Championship in Chicago during the summer of 2010.

Following the end of his senior season, Zeller was named Indiana Mr. Basketball, the state's highest honor for high school players and an award both of his elder brothers also won.

He was a 2011 McDonald's All American player and scored 10 points, pulled down three rebounds and had three assists in the nationally acclaimed all-star game.

[9] On November 12, 2010, Zeller committed to play for Indiana University, turning down offers from North Carolina and Butler.

[15] 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.

Although projected to be a top ten pick in the 2012 NBA draft, Zeller decided to return for his sophomore season at Indiana, along with teammate Christian Watford.

"[15] Due in part to Zeller's leadership, the Indiana Hoosiers finished the 2012–13 season as the outright Big Ten champions.

At the end of his sophomore season, Zeller decided to enter the 2013 NBA draft,[18] along with teammate Victor Oladipo.

[27] Despite missing the entire preseason because of a right knee injury, Zeller played in the Hornets' season opener on October 26, 2016, going 5 of 6 from the field for 15 points in 14 minutes in a 107–96 win over the Bucks.

On February 6, 2025, Zeller and a 2028 second round pick were traded to the Houston Rockets in exchange for the draft rights to Alpha Kaba.

[52] In college, analysts described Zeller as having "the outstanding combination of mobility, scoring instincts and aggressiveness", while also being "an incredibly agile and fluid big man who runs the floor well and has the explosiveness to play above the rim regularly.

[2] Other commentators have noted his "high motor" and that he is "the best screen-and-roll frontcourt player in college basketball...He sprints to the screen, reads slips, and has great hands.

[54] Despite pressures brought on by unusually high expectations, commentators have noted his humility and work ethic, along with "dry wit and prankster's mirth.