The experienced forward has been training with the Addicks for the last few weeks and scored in a recent friendly against QPR.
The 31-year-old, who has been without a club since his release by Ipswich at the end of last season, is available for Tuesday night’s game against Peterborough.
Charlton boss Karl Robinson told the official website: “Leon is in the top three runners at the football club, from a speed perspective. He’s very, very quick and powerful.
“He’s been great around the building in the last few weeks and it is something that he really wanted to get done.
“Besty is a great character. He’s been there, seen it, done it at the highest level and, listening to him, he feels like he has a point to prove to three or four people.
“He’s very hungry and that is the thing that sealed it for me – that’s he’s really excited about moving forward and trying to play for Charlton.”
Best, who has played for Sheffield Wednesday, Derby, Brighton and Newcastle amongst others, said: “I’m really excited and hopefully I can come in and make a difference on the pitch.
“I’d like to thank the manager and the staff. When I first came in to train, I wasn’t in a position to be signed. They’ve really helped me to get fit and never put any pressure on me or tried to rush me, and hopefully now I can repay them.”