The midfielder had been a free agent for a short period of time following his release by Coventry City.
"I'm delighted. I was looking to sign for a good team and I think I've found this in Charlton," he told the club's official website. "I had a phone call to come and have a chat with the manager and meet the people here and I had a good feeling straight away.
"I've played against them before and The Valley is a great stadium so as soon as I heard of the interest it happened really quickly after that."
Moussa scored 14 goals for the Sky Blues last term.