"It's just a good place for me all around with the development of my game and chance to play at a high level," Allen told ESPN's Joe Schad.
Allen started the first three games for LSU in 2013 and appeared in all 13 after missing most of 2012 with a knee injury. He posted 16 tackles and two sacks in 2013. He has one year of eligibility remaining and must enroll in a graduate program not offered by LSU.
Arizona declined to comment on Allen's arrival.