Henson is a sophomore from Florida and Zeller is a junior from Indiana. Both forwards were second-team All-ACC selections in 2011.
Freshman Harrison Barnes of Iowa has not announced his intentions. He may choose to declare for the NBA Draft.
"I want to come back to school next year because I enjoy all aspects of being a college student and I truly love being a Tar Heel," Henson said.
Zeller says he wants to finish his college career and graduate.
"I came to Carolina because it had the balance of academics and basketball I wanted and it was the best place for me to prepare for life and a career in the NBA," Zeller said. "That's exactly what we have here. I want to finish my college career, compete for championships and graduate on time."
UNC head coach Roy Williams says he delivered the news to NBA teams on behalf of Henson and Zeller and continues to gather information on behalf of Barnes.
"I spoke to about 10 NBA teams on their behalf and gave them that information, but their individual decisions are less about the NBA and more about what they wanted to do right now and the experiences they are enjoying at the University of North Carolina," Williams said. "Harrison is not as far along in his decision-making process as were Tyler and John. I am still gathering information on him from NBA teams and hope to provide him with all of that information by the end of next week.
The Tar Heels ended their season with a trip to the Elite Eight where they were defeated by the Kentucky Wildcats.