The Bulgarian international striker, 27, has signed a four-year contract after joining from Tottenham Hotspur for an undisclosed fee.
As part of the deal, United striker Fraizer Campbell will spend the rest of the 2008/09 season on loan at White Hart Lane.
Upon becoming a United player, Dimitar told ManUtd.com: "Joining Manchester United is a dream come true for me. I look forward to playing my part in helping this club win more honours in the years to come."
Sir Alex Ferguson was delighted to finally capture the elegant striker and admitted: "This is a key signing. Dimitar is one of the best and most exciting strikers in world football.
"His style and ability will give the team a different dimension and I’m sure he will be a popular player with the fans."