Macheda, in the final year of his contract at United, watched Rovers' goalless draw with Yorkshire rivals Huddersfield from the directors' box at the John Smith's Stadium on Saturday and reported for training at the Sky Bet Championship club's Cantley Park complex on Monday morning.
The south Yorkshire club announced on their official website on Monday: "Doncaster Rovers have agreed a deal with Manchester United to take 22-year-old Italian striker, Federico Macheda, on an initial one-month loan with the option to extend it, subject to paperwork."
Macheda could now be a part of Paul Dickov's squad for Doncaster's league trip to Watford on Tuesday night.
The Italian has failed to live up to his early promise since bursting on to the scene with a superbly-taken last-minute goal on his debut to earn United a 3-2 victory over Aston Villa at Old Trafford in April 2009.
Loan spells with QPR, Sampdoria and Stuttgart, where he spent the last five months of last season, have followed but the 22-year-old has struggled to score goals at all three clubs.
Macheda's last appearance for United came last December in a Champions League defeat to FC Cluj where he came on as a second-half substitute.