The 25-year-old put pen to paper on a two-and-a-half-year deal at Whaddon Road just minutes before the 11pm deadline in the January transfer window.
Harrison has scored eight goals in 28 games for a struggling Dons side and could make his debut against Torquay at the weekend.
Harrison's arrival comes after Robins boss Mark Yates added Luke McCullough, Jason Taylor, Michael Hector and Paul Benson to his squad.
Meanwhile, Alan Bennett and Jeff Goulding have left by mutual consent.
Yates told the club's official website: "I'd like to thank both for their efforts and service to this club."