Parker takes over a club lying second bottom of the Premier League and with only one win from their last eight league fixtures.
"Scott's immediate assignment is merely to help us stabilise, grow and rediscover ourselves as a football club," Fulham chairman Shahid Khan told the club's official website.
"If Scott can answer that challenge, and our players respond to the opportunity, perhaps victories will follow in the months ahead."
He rejoined Spurs as manager of their Under-18s before going to Fulham last summer as first-team coach.
Parker's first match in charge will be on Sunday when Fulham host Chelsea.
Ranieri had taken over in November, guiding Fulham to victory over Southampton in his first match and nine points from his first eight. They could not maintain that form.
"Claudio's tenure at Fulham didn't produce the outcome we anticipated and needed when I appointed him as manager in November, but be assured he is not solely to blame for the position we are in today," Khan said.