The English champions have been linked with a move for the 18-year-old since the summer but have now officially confirmed that Possebon is a United player.
"Sir Alex Ferguson has handed United's number 34 shirt to Brazilian youngster Rodrigo Possebon," read a club statement.
"The 18-year-old midfielder, who completed a transfer from Sport Club Internacional last month, is expected to keep learning his trade in United's reserves, but will now be eligible for senior duty if required."