The 18-year-old midfielder, who has signed a three-and-a-half-year deal, was the subject of a rejected bid from Newcastle United earlier in the month.
BBC Sport understands the deal does not include a buy-back option.
The highly-rated youngster, whose Old Trafford contract would have run out this summer, was part of United's FA Youth Cup winning side last year.
But United boss Sir Alex Ferguson recently branded Morrison's contract demands as "unrealistic".
Ferguson handed the Wythenshawe-born player his senior debut in the Carling Cup in 2010 against Wolves, but the youngster has also had a chequered history off the pitch.
Two days after winning the 2011 FA Cup Youth final, the 18-year-old was fined £600 by a court for throwing his girlfriend's mobile phone through a window during an argument.
And Ferguson is hoping a change of scenery will help Morrison put his off-field problems behind him.
"In the case of Ravel it's been quite well documented," said Ferguson. "I think he's better out of Manchester.
"He's got a great talent but it's how to deal with it that is important."
Morrison told the Hammers website: "I'm really pleased to have signed. The move has happened very quickly and I'm looking forward to hopefully moving up to the Premier League with West Ham soon.
"I'm an attacking player and I'm hoping to get the fans on their feet."
West Ham United have signed Manchester United's Ravel Morrison for an undisclosed fee.