The Championship club retain the option to extend the Italian's deal, and he is likely to make his debut on Tuesday when Doncaster travel to Vicarage Road to face Watford.
Macheda, 22, made his debut for the Old Trafford club in a 3-2 victory against Aston Villa in April 2009, a game in which he scored the winning goal in the dying stages.
But he has failed to establish himself as a first-team regular at the Premier League champions, spending time on loan with Sampdoria, QPR and Stuttgart in the past.
Doncaster manager Paul Dickov was delighted with the signing and believes Macheda is hungry to prove himself.
"It's a massive coup. We've got him for an initial month with a view to extending it to the 93 days, which is the maximum," Dickov told BBC Radio.
"I know from speaking to Sir Alex Ferguson and David Moyes he's a top quality player and David knows we'll look after him and keep him informed on his progress.
"We had a little nibble at him before the season started, but it wasn't to be then.
"Hopefully he'll add goals. He's been to big clubs on loan but not really played for them, and he's very hungry to get his career back on track."
