British media reported that Fulham had agreed to pay around £20 million plus add-ons for Berge, whose acquisition strengthens their midfield following Joao Palhinha's move to Bayern Munich.
"It feels fantastic. It's been a little bit back and forth the last few weeks but I'm finally sitting here in the shirt in this beautiful stadium, knowing that my future is here, which feels great," Berge said.
"The DNA of the club is to be dominant, aggressive, front-footed and play nice football, and I think that suits me."
Berge joined Burnley in 2023 from Sheffield United and made 37 appearances in the Premier League last season but was unable to help the Lancashire club avoid relegation.
He has played 46 matches for the Norway national team, scoring one goal.
