Macheda, in the final year of his contract at United, has joined Rovers on an initial one-month loan deal.
The Italian, 22, watched the goalless draw with Huddersfield from the directors' box at the John Smiths Stadium on Saturday and reported for training at the Sky Bet Championship club's Cantley Park complex on Monday morning.
He is expected to go straight into Dickov's squad for Doncaster's league trip to Watford on Tuesday night.
Speaking about the signing, Dickov said: "I think it's a massive coup for this club.
"We've got him for an initial month with a view to extending it to the 93 days, which is the maximum we can do.
"His record over the last couple of years is slightly misleading because he's been at a couple of top clubs on loan but not necessarily went there and played.
"I know from speaking to Sir Alex Ferguson and David Moyes that he's a top quality player and he's a finisher.
"He's different to what we've got. Technically he's very good, he can hold the ball up, but we want to get him in the box because that's where he's at his best."
Macheda 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 five months of last season, have followed but he has failed to score a single goal at any of the 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.