The League One promotion chasers have sealed a deal for Cole, who only joined Fulham from Manchester United on deadline day in January.
The winger played in the Cottagers' recent 2-2 draw away to United in the Premier League, but has not been involved since Rene Meulensteen left the club.
Sky Sports revealed earlier on Tuesday that a deal had been agreed and now the two clubs have confirmed the 20-year-old's switch.
"I'm really excited by this signing," MK boss Karl Robinson told the club's website.
"We've been watching Larnell for a while and he is a high-potential player."
Cole, who can play anywhere in midfield and also at full-back, will go straight into the Dons squad for Tuesday night's League One clash away to Oldham. His arrival is a significant boost for Robinson after the loss of Samir Carruthers to a knee injury.
"We had to react quickly to the Samir injury," added Robinson, "and he's exactly the type of player I want to bring to the football club - a player of quality, a player of note."