Weaver, 28, has put pen to papaer on a three-year-deal at the Valley, after leaving Manchester City, where he made over 200 appearances.
Striker Todorov, also 28, has penned a one-year-deal.
"They're two proven Premiership players who are now Championship players," boss Alan Pardew told Charlton's official website.
"Nicky hasn't had the breaks in his career that he has deserved, but this is a great opportunity for him while Svetoslav's quality and precision, which is proven in this division, will be very important to us, especially in home games."
The pair are the seventh and eighth signings of the summer.
"Leaving Portsmouth was a big decision for me but I'm looking forward to playing for Charlton," Said new signing Todorov.
"I like the way Alan Pardew's teams play. I saw his teams at Reading and at West Ham and liked their style."
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