The Italian is in his final year at Manchester United, and watched Doncaster's goalless draw with local rivals Huddersfield on Saturday, and then attended the club's Monday morning training session at Cantley Park.
The Rovers confirmed on their official website that a deal had been done to bring Macheda to the Yorkshire club.
Macheda could now feature in The Vickings' squad for their mid-week trip to Watford on Tuesday night.
Federico has failed to establish himself at United after showing early promise and bursting on to the scene with a superb last minute goal on his professional debut against Aston Villa in 2009.
Macheda's last first team appearance for Manchester United was in December of last year in a Champions League group-stage game, United lost 1-0 against FC Cluj.
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