The 23-year-old became a free agent this summer after his AZ Alkmaar deal expired at the end of last season, and Charlton have moved quickly to secure the Iceland international's services.
"I'm excited to be here," Gudmundsson told the club's official website. "It's a new challenge for me and I can't wait to start training with the lads.
"I heard of the interest a few weeks ago and obviously I'm on a free transfer so there were a lot of things happening, but in the end I decided to go with Charlton.
"It's a great club with a good history and I think we are building something good here."