The Under-23s captain has signed a two-year contract at Bradford City as he looks to push on with his professional career.
The club confirmed the player's departure on Friday afternoon and Riley thanked supporters in a post on his personal Twitter account, saying: "Manchester United has been my home, my family for the last 15 years. It is every boy's dream to play for this club and I can proudly say I have achieved this.
"I want to take this opportunity to thank everyone, from all the coaches that have helped me along the way, the staff, the many players I've played along side whilst growing up but most importantly the fans that have showed constant support throughout my whole time here.
"I have so many unforgettable memories and experiences that I'll forever be grateful for but I personally feel right now is the right time for me to move on and to start the next chapter of my career. I wish everyone at the club the very best, and again thank you."
Bradford announced the arrival of Riley on their club website, and head of recruitment Greg Abbott spoke of his delight at signing the youngster, saying: "Joe has been on our list of potential signings for a long time now.
"He ticks a lot of boxes in terms of the way the club wants to go and he really fits the model.
"He was flying at the time but unfortunately got a shoulder injury.
"He has bags of pace and energy, he is a forward-thinking, attacking full-back.
"Joe has always been high up on our list for that position."