After turning down the offer of a new contract with League One side Gillingham the 32-year-old will look to add to his total of 124 goals with the London club next season.
Twice a Northampton Town player, Akinfenwa is due now to return to Sixfields on the opening day of November when his new side are the visitors.
Dons boss Neal Ardley said: "Adebayo will probably divide opinions in many ways, but I think it's key to point out that he can play football. He's not just a big man who can win headers."