Financial details were not disclosed by either club, but British media reported that the deal was worth around £30 million.
The 28-year-old, capped 36 times for Denmark, had joined Palace in 2021 from Ligue 1 club Lyon, making 113 appearances across all competitions for the Selhurst-based side.
He also spent the 2020/21 season on loan at Fulham and will wear the number five shirt, the same number he wore during his previous spell at the club.
"It's really nice to be here. Feels a little bit like coming home, so it's a good feeling," Andersen told FFCtv.
"I know the club, I know how Fulham are playing, I know many players, I know some staff, so I didn't need anyone to convince me because I knew a lot of things already.
"I had some good talks with the manager. I know the playing style he likes to play, so it was just a decision I needed to make myself, with my wife and family, and see what's the best for me, and I think this is a good step for my career."
Fulham, who finished 13th last season, next host promoted Leicester City in the Premier League on Saturday, having lost to Manchester United 1-0 away in their season opener.
