Fulham sit 19th in the Premier League following their 2-0 defeat at Southampton on Wednesday evening.
Ranieri took over in November, replacing Slavisa Jokanovic.
However, the former Leicester manager struggled to turn things around in west London.
Ranieri won just three of his 16 league games during his time at Craven Cottage.
Fulham are now 10 points off safety with just 10 games remaining this season.
And the Premier League strugglers have now confirmed Ranieri’s departure, revealing Parker will take over as caretaker manager.
A statement from the club read: “Following our discussion this afternoon, Claudio Ranieri agreed to my decision that a change was in the best interest of everyone.
“No surprise to me, Claudio was a perfect gentleman, as always. 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.
“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.
“I am asking Scott Parker to serve as our Caretaker Manager. 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.
“What’s most important at this moment, however, is to regroup in a smart and deliberate manner that will serve our long-term vision for sustainable success.
“If we’re able to do that and win some matches to make a stand late in the season, all the better.”
Ranieri also opened up on his departure, thanking the supporters and the club for the opportunity.
He 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.”
Fulham are back in action on Sunday against Chelsea in the Premier League.