Scotland winger Forrest drilled home early in the second half at Celtic Park to register for a fifth straight game in all competitions.
Edouard then ensured a deserved victory for Neil Lennon's side, who had suffered a disappointing exit in Champions League qualifying to Cluj, and the final margin of victory would have been even greater were it not for visiting goalkeeper Oscar Linner.
Celtic thought it had the lead when Edouard turned home Ryan Christie's throughball, only for the offside flag to curtail the celebrations.
Michael Johnston was thwarted by Linner at the end of a nicely worked move and the visiting keeper was also sharp to turn Edouard's edge-of-the-box drive wide.
Callum McGregor saw a rasping drive tipped over by Linner shortly after the restart, but the keeper was unable to prevent Forrest's 48th-minute effort finding the back of the net despite getting strong hands to the shot.
There was no coming back for AIK when Edouard curled home a superb 25-yard free-kick into the right side of the goal, giving Linner no chance.
Linner kept out McGregor and Edouard late on, but Celtic still have a comfortable cushion to protect in next week's return fixture in Sweden.