Nichols made the announcement Tuesday afternoon on ESPN Radio 92.9 in Memphis, Tennessee.
"It was in the best interest of my family and I to decide to transfer from the University of Memphis," he told the radio station. "I want to thank everyone for supporting me in my two years at Memphis. The coaching staff, fans, family and friends. As for me, I think it's best if I move on from here."
Nichols, who averaged 13.3 points and 6.1 rebounds last season before suffering a season-ending ankle injury, was expected to be a candidate for American Athletic Conference Player of the Year. He informed Tigers coach Josh Pastner of his decision about a week ago, sources told ESPN.
Memphis has refused his request to transfer due to the timing. All of the high school players for this season have made their decisions, and there are few high-level transfers left as well.
"The school isn't going to release him,'' Pastner told ESPN's Andy Katz on Tuesday night. "We spoke with Austin in mid-June and everything was fine. We named him captain after the season. We don't know what has changed.''
Pastner said the entire coaching staff was caught off guard by the decision.
"He's a potential player of the year in our league. He's been nothing but great the first two years we have had him,'' said Pastner. "He's been terrific on the floor.''
Pastner said the president and athletic director support the decision not to release him. He added that the staff hasn't heard from Nichols since he made his announcement.
The coaching staff is supposed to head off on the road recruiting Wednesday for the first July evaluation period, but now has a gaping unexpected hole for the upcoming season.
Nichols' departure would be a huge blow to Pastner and the program. Memphis finished 18-14 last season and 10-8 in league play, and the Tigers failed to make the NCAA tournament for the first time in five seasons.
Information from ESPN's Andy Katz was used in this report.