Williams was a first-team all-Big Ten selection last season and one of five finalists for the Kareem Abdul-Jabbar Award, which goes to the nation's top college center, when he averaged 15.5 points, 9.1 rebounds and 2.3 assists while recording 11 double-doubles.
"I would like to thank the organizations that gave me the time to work out for them and to go through this process with them the last couple of weeks," Williams said. "The feedback and instruction that I received will be very beneficial as I continue to improve as a basketball player. I am excited to return to Purdue for my senior season, to earn my degree and help this program in any way possible."
The 6-foot-10 Chicago native was a first-team all-Big Ten selection last season and his six 20-point games ranked No. 3 nationally among major-college players.
Williams' return means Purdue will have all five starters back from a team that went 18-10 and earned a No. 4 seed in the NCAA tournament.
"Trevion has put in a lot of time on getting his body right and working on his game," coach Matt Painter said. "He will obviously have a big role for us next season."