The 36-year-old has been out of work since October after he left MK Dons following a six-year spell in charge of the club.
Robinson guided the Dons to automatic promotion to the Championship at the end of the 2014-15 season, but they lasted just one campaign in the second tier before suffering relegation.
Now, the Liverpool-born coach has taken up a new job at Charlton, who are currently 11th in League One after 18 games.
"I am honoured to have been appointed manager of Charlton and can't wait to get started," Robinson told the club's official website. "Joining such a huge club with a large, passionate fanbase is a really exciting proposition.
"I've inherited a talented squad and I'll be doing everything I can to get the club back into the Championship as soon as possible.
"I like my teams to play attractive football and if we all pull together, I firmly believe we can start moving up the table and enjoy a successful season."
Charlton chief executive Katrien Meire added: "Following a thorough appointment process, Karl emerged as the outstanding candidate. He is a very talented, forward-thinking Manager and I'm delighted we have been able to bring him to Charlton.
"Our main focus is bringing Championship football back to The Valley at the earliest opportunity. Karl has vast experience of League One and, having won promotion just two seasons ago, we believe he has the necessary credentials and is best equipped to lead the club forward.
"Throughout his time with MK Dons, Karl received tremendous acclaim throughout the game for the attractive football his teams played and his approach to developing young players. This is an exciting appointment for us."
Robinson, who will begin his new job on Monday, replaces Russell Slade, who was sacked last week after just six months in the role.