The 20-year-old had spells on loan at Torquay and Dagenham last year, finding the net five times in 25 appearances, and was also borrowed by Leyton Orient and Wycombe in 2013.
After just one appearance for Charlton he was released in the summer and his addition to the Dons' attack provides competition for the experienced Adebayo Akinfenwa and Matt Tubbs. Dons manager Neal Ardley told the club's website: "He fits the profile we were looking for after bringing in two big strikers. We wanted the third forward to be a young striker who we could develop with different attributes.
"Ade is very fit, energetic and quick and he's a good size. He's also got League 2 experience and last season he got three goals in 15 games at Dagenham, but sometimes he played wider in a front three.
"We are going to play two strikers whenever we can next season and Ade gives us a great option with his pace.
"He's a player who is different to the other two- we have someone who is a very good at holding the ball up and another who is an outstanding finisher. If Ade cannot learn from those two then I'd be very surprised."
Azeez added: "I'm delighted and words cannot express how happy I am to have signed. I've heard good things about Neal Ardley from when Michael Smith [former Charlton team-mate] was here. He gave me really good feedback about how working with Neal improved him as a player.
"I want to start the hard graft as soon as possible."