Gary McAllister said: "I've spoken with Leon and like a number of players I can't guarantee them regular football.
"Leon is at a stage in his career where he needs to be playing regular football and hopefully this move will enable him to do that."
Constantine had a loan spell at Oldham torwards the end of the season, scoring twice in eight appearances.
Constantine broke his ankle, cracked his toe and fractured his arm during an ill-fated campaign with the Whites and didn't feature at all under McAllister following his arrival.
Speaking in the YEP, Constantine said: "It's one of those things that happens in football. I'd rather go somewhere where I'm going to be part of everything.
"At the end of the day, I wasn't one of his signings. He's going to do what he thinks is right and bring in his own players. He knew I didn't want to sit about and not play and he was honest with me and credit to him for that. It's just the way it goes.
"It's a shame really. I still had a great time at the club and the supporters have been unbelievable and I can't thank them enough.
"For me, it's great to have been part of a big club like Leeds, but sometimes you've just got to go a different way."