The 23-year-old left the Dutch outfit at the end of last season after making 145 appearances across four seasons with the club, scoring 13 goals.
Gudmundsson, who has represented Iceland on 32 occasions, is Charlton's second signing of the day following the arrival of Tal Ben Haim.
"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."