He has come to a settlement with the Albion, which sees the final year of his contract terminated.
Hemed can now sign for the Championship side outside of the transfer window, as he is a free agent. It ends his four-year stint at Brighton.
Albion coach Graham Potter said: "At this stage in his career Tomer wants to play regular football and at Charlton he has the opportunity to do that.
"There's no doubt he's been a great player for this club. He played an integral part in winning promotion from the Championship, and scored some crucial goals in the Premier League.
"During the short time I've been here, he's been a fantastic professional. On behalf of the club I'd like to thank him for his service and wish him all the very best for his time with Charlton and his future career."