Macheda watched Doncaster's draw against Huddersfield from the directors' box on Saturday and reported for training with Paul Dickov's team after sealing the switch.
Macheda, 21, has made just 22 Premier League appearances for United, scoring four goals, as well as four appearances in the Champions League.
A Federico Macheda brace helped Premier League champions Manchester United canter to a 4-1 win over New England Revolution on Wednesday, as big money new signing Ashley Young made his debut.