Meulensteen was on Wednesday named as Fulham's head coach, working alongside under-pressure manager Jol, whose side are languishing in the Barclays Premier League relegation zone after a run of just three wins in 11 games.
Meulensteen, who left Manchester United's coaching team in the summer following Sir Alex Ferguson's departure, will take up the role immediately.
The appointment of the 49-year-old will raise as many questions over the future of Jol as it answers, with the arrival of Meulensteen sure to be seen by some as a move that dilutes Jol's authority.
However, Meulensteen insists Jol had played a key role in bringing him to the club, and Fulham's Twitter feed on Wednesday posted a picture of the two Dutchmen in which the Fulham boss was grinning broadly.
"I have spent many hours talking with Martin Jol and we share a vision of how football should be played and how players should be developed," said Meulensteen, who had been touted as a possible replacement for Ian Holloway at managerless relegation rivals Crystal Palace.
"It is our job to make sure we can bring this vision to life on the pitch for the fans."
Fulham chief executive officer Alistair Mackintosh said Meulensteen, who lasted just 16 days as boss of Anzhi Makhachkala earlier this season amid off-pitch upheaval at the Russian side, was one of the "best coaches in the world".
"We are all delighted to welcome Rene to Fulham," Mackintosh said.
"There was always going to be a battle for Rene's services and, with the assistance of our chairman Shahid Khan, we have been able to bring one of the best coaches in the world to Fulham."
Meulensteen's coaching career began at NEC Nijmegen in the early 1990s before working extensively in the Middle East over the following decade.
He joined Manchester United in 2001, first as a youth coach and later working with the reserves. He left Old Trafford to take up a role at Danish side Brondby in 2006 but was back at United the following year, rising to the role of first-team coach by 2008.
Meulensteen was a key part of the United set-up that won the Premier League in 2009, 2011 and 2013, and was also involved in the team's 2008 Champions League triumph in Moscow.
Ferguson's departure from United earlier this year heralded the end of Meulensteen's time at United, with incoming manager David Moyes preferring to assemble his own coaching set-up.
Meulensteen joins Fulham amid a bleak run of form that has seen the pressure mount on Jol.
The Cottagers have lost their past three league games to sink into the bottom three, while they have conceded seven goals in their past two defeats to Manchester United and Liverpool.