"I'm really excited to be here," Sinclair told Charlton's official website.
"There were a few clubs in for me, but I thought Charlton would be the right one for me and I'm sure I've made the right choice."
Sinclair, who turns 19 next month, has made seven appearances for Chelsea this season and will be available for the Championship play-off final should Charlton be involved.
"I've had a few starts for Chelsea, but it's been frustrating trying to break though there, with all the good players they have," he added.
"That's why I've chosen to come to Charlton. It's a club that seems ready for the Premier League, and I think with the squad that we have got we can definitely reach it."