LSU athletic director Joe Alleva said Johnson is leaving the Tigers after four seasons to take another head coaching position.
Alleva didn't say where Johnson was headed, but TCU said Sunday that a "major announcement" involving its men's basketball program would be made during a news conference on the Fort Worth campus Monday afternoon.
There were no other specifics given in the TCU release, but a person with knowledge of the situation told The Associated Press that Johnson would be hired as Jim Christian's replacement. The person spoke on condition of anonymity because no official announcement was made.
"Sometimes coaching changes work out well for all parties involved, and we will take this opportunity to seek out the best coach for the long-term future of LSU men's basketball," Alleva said. "We will move quickly but deliberately to find a coach who will lead our program with integrity and discipline, someone who will recruit effectively in order to build championship teams while inspiring success in academics, and someone who will energize our fan base. I wish Trent all the best in his new job."
Johnson's introduction at TCU will come a week after officials there said Christian was leaving after four seasons.
Christian was hired Tuesday as the coach at Ohio University. He returned to the Mid-American Conference where he won at least 20 games in each of his six seasons at Kent State and took the Golden Flashes to two NCAA tournaments before moving to TCU.
The Horned Frogs are moving next season from the Mountain West Conference to the Big 12.
Johnson had a 67-64 record in four seasons at LSU. He previously took Nevada and Stanford to the round of 16 in the NCAA tournament.
TCU hasn't been to the NCAA tournament since 1998 when Billy Tubbs was its coach.
Christian was 56-73 at TCU. But the Horned Frogs were 18-15 last season, their first winning season since 2004-05. They finished the season with a second-round loss at Oregon State in the College Basketball Invitational tournament.
LSU was also 18-15 last season, and lost to Oregon in the first round of the NIT.
When Johnson got to LSU in 2008, he had a team filled with seniors. The Tigers went 27-8 and won the SEC regular season championship his first season, but went 22-41 combined with only five SEC wins the next two years.
Johnson went to LSU from Stanford after taking the Cardinal to three NCAA tournaments in four seasons. Stanford, a private school like TCU, was 28-7 and went to the NCAA round of 16 in 2007-08, his final year there.
Nevada also went to the round of 16 in Johnson's final season, 2003-04 when the Wolf Pack were 25-9. He was 79-74 at Nevada from 1999-2004.
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