The Italian’s last game was Wednesday’s 2-0 defeat by Southampton, which left the Cottagers 19th in the Premier League, 10 points from safety with 10 games left.
Ranieri took over in November after the sacking of Slavisa Jokanovic.
The 67-year-old won only three of his 17 games as manager.
It included a 3-2 victory over Southampton in his first game, but 11 defeats have followed including an FA Cup third-round exit at home to League Two side Oldham.
Chairman Shahid Khan said in a statement: “Claudio walked into a difficult situation, inheriting a side that gained only one point in its prior eight matches, and he provided an immediate boost by leading our club to nine points in his first eight matches as manager.
“Though we were unable to maintain that pace thereafter, I am grateful for his effort. Claudio leaves Fulham as our friend and he will undoubtedly experience success again soon.
“Scott’s immediate assignment is merely to help us stabilise, grow and rediscover ourselves as a football club.
“If Scott can answer that challenge, and our players respond to the opportunity, perhaps victories will follow in the months ahead.”
Ranieri led Leicester City to a miraculous Premier League title triumph in 2016, but was sacked just nine months later and then had a season in charge at French Ligue 1 side Nantes.
He took over on a “multi-year” contract at Fulham when they were bottom of the table with five points from their opening 12 matches, but failed to oversee an upturn in fortunes.
Ranieri added: “I am obviously disappointed with the recent results and that we could not build on the good start we made following my appointment. Finally, I would like to thank the club, the players and the fans for the support they have given me during my time at the club.”
The 38-year-old, capped 18 times by England, has no previous managerial experience but played nearly 600 professional games, mainly in the Premier League for Charlton, Chelsea, Newcastle, West Ham and Tottenham, before ending his career at Fulham in June 2017.
A year later he returned to the club as first-team coach, having been in charge of Tottenham’s Under-18 side.