Richardson had a trial at Old Trafford last season and impressed enough to catch their eye.
In March, he tweeted: "Good debut for Man Utd today, thought the boys were class and we deserved more from the game! On to the next one."
The 18-year-old, who was out of contract at Leeds in the summer, has now signed a permanent deal and according to Man Utd's website will join up with the under-23s and the UEFA Youth League squad.
Richardson is expected to play in the Super Cup NI tournament, which kicks off in Northern Ireland this week.
