Randolph, a 6-foot-10, 205-pounder, was an honorable mention All-American in his first year with the Tigers, averaging 15.6 points, 8.5 rebounds and 2.3 blocked shots per game. He was a unanimous SEC All-Freshman Team pick by the conference's coaches.
"After much discussion with my family and those closest to me, I feel that there cannot be a better time for me to enter the NBA draft," Randolph said at a news conference Tuesday.
LSU was 13-18 record this past season. Coach John Brady lost his job and the Tigers missed the NCAA Tournament for the second straight season.
Randolph can return to school for his sophomore season if he does not hire an agent and withdraws his name from the draft prior to the June 16 deadline.