The Premiership champions have forked out £3.5 million to lure the midfielder to Old Trafford with the French outfit receiving an additional £700,000 depending upon appearances.
Djemba-Djemba successfully passed a medical on Thursday morning and signed a five-year contract with The Red Devils.
The 22-year-old revealed it was the fulfilment of a dream to clinch a move to Old Trafford and is eagerly anticipating the start of the new season.
‚Ç£This is a very proud moment for me," Djemba-Djemba told the club's official website.
"Ever since I was a teenager it has been my dream to play for Manchester United.
"If the club is signing me it is because they really believe in me. I am here to learn and to work hard, and I cannot wait for the new season to start.‚Ç¥
Red Devils manager Sir Alex Ferguson was delighted with his new signing and is confident Djemba-Djemba will be a valuable addition to the club's ranks.
Ferguson said: ‚Ç£Eric is a young player we've watched throughout the season, and he's impressed us each time with his understanding of the game.
"He's quick, aggressive and a good passer of the ball, and is the kind of athletic footballer we are looking for.
"In the last few months he has shown his development playing in a very good Cameroon team, and he looks like a Manchester United player in every sense."
