The 20-year-old has signed a four-year contract and has joined the club for a fee believed to be around £3million.
Obertan is Sir Alex Ferguson’s third signing of the summer, following the recent arrivals of Michael Owen and Antonio Valencia.
“Gabriel is a player we have tracked for a few years now, but because of his educational programme our efforts to get him here have always been delayed,” Fergie told the club’s official website.
“We are delighted to get him now as he is an exciting prospect. We like to get young players and develop them, and we will see that in Gabriel over the next two years.”
“I am very happy to join Manchester United,” Obertan added. “This is a big opportunity for me to play at such a great club. I am very excited to be here and I look forward to proving what I can do.”