The 30-year-old scored 22 goals in 187 appearances for the Shakes after moving to Gigg Lane in 2012.
Former Crystal Palace and Stoke man Soares becomes Wimbledon's first signing of the January transfer window.
"Tom is very powerful, has good aerial ability and I think he is in his prime now," Dons boss Neal Ardley told the club website.
The south-west London club have not disclosed the length of Soares' deal at Kingsmeadow.
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AFC Wimbledon have signed midfielder Tom Soares from fellow League One side Bury for an undisclosed fee.