The 6-foot-1, 220-pounder is considered a top-five pick for this year's draft. Some online mock draft boards have Peterson rated as high as the second over-all pick in the draft.
"Peterson's draft position is really too good to forgo," said Tigers coach Les Miles. "I agree with his decision completely."
Peterson's younger brother,Avery Johnson, is committed to play for LSU.He recently completed his junior season at Pompano Beach's Blanche High School, the same school that produced Peterson.
Peterson had 43 tackles,four interceptions and 10 passes broken up as a junior. He also excelled as a kick returner, averaging 29.1 yards a kickoff return and 16.1 per punt return with two touchdowns.
Peterson was a first-team All-American and won the Bednarik Award, given to the nation's top defensive player.
He made the announcement at a news conference at LSU.
Miles will meet Michigan officials on Tuesday about their vacant head-coaching job.