The club's billionaire owner Shahid Khan switched one Dutchman with another on Sunday, as Jol departed Craven Cottage after two and a half years in charge to be replaced by a former trusted lieutenant of Sir Alex Ferguson.
Fulham will hope some of former Manchester United boss Ferguson's magic has rubbed off on the 49-year-old, whose experience in management is limited but whose reputation as a coach is among the best.
Khan decided Jol had to go after Saturday's 3-0 loss at West Ham, a sixth defeat in a row for the Cottagers. Five of those losses have come in the Barclays Premier League, with Fulham consequently plummeting into the relegation zone.
Meulensteen came in only last month to serve as head coach under Jol, and has benefited from seeing where the team's deficiences lie as he prepares to start work in the top job.
His task is to steer Fulham clear of danger and preserve the top-flight status they have maintained since 2001.
"It's a massive challenge," Meulensteen told Sky Sports News. "But when you're faced with a challenge like this it comes down to making sure you get the basic things right.
"You need to stay mentally strong and make sure the fans are getting behind the team.
"We need to make sure the players are mentally strong and believe."
He added: "I am confident because of the sort of experiences I've had for so many years at Manchester United.
"I know what is required at the top end of the Premier League.
"This is a different challenge with different pressure. This is making sure you realise the need to keep three teams below you.
"Don't even speak about getting into the top six, top 10, whatever it is.
"You need to make sure you close your ranks, and you make sure you start winning again.
"We need to make sure we don't start conceding easy goals which Fulham have done in the last two games and the games before."
Meulensteen, whose first match in charge will be the home fixture against Tottenham on Wednesday, graduated through the Old Trafford ranks, becoming first-team coach in 2008, a post he held until Ferguson retired at the end of last season.
A short stint in charge of Russian side Anzhi Makhachkala followed, and Meulensteen was strongly linked with Crystal Palace before Tony Pulis took over at Selhurst Park.
Jol and Meulensteen have spoken since Khan dismissed the former Tottenham and Ajax boss.
"I rang him straightaway," Meulensteen said.
"I said to Martin, 'Listen, I don't know if this is anything to do with me, but in the time I worked 12 years with Manchester United, and for five to six years with Sir Alex Ferguson, I had no problem, but I go to Anzhi and Guus Hiddink departs after two weeks, and Martin does the same'.
"I don't know if was anything to do with me, but it was definitely not something I was anticipating.
"We wanted to turn this corner together."
Jol will have his chance to say farewell to the players and Meulensteen reported his predecessor was "still full of desire and fighting spirit" during their conversation.
"I'm not a great supporter of this kind of decision," Meulensteen said, "but this is what happens and we need to look to the future now.
"We need to make sure we make every decision that will increase the chances of making sure that Fulham is a Premier League club next year. That's where they belong and that's what we need to do. If there are investments need to be made in whatever area, we need to live up to that, otherwise you might be paying a high price."
Many supporters had been on Jol's back, calling for change, and Khan decided the London derby loss marked breaking point.
Khan said in a statement on Fulham's website: "Today I spoke with Martin to thank him for his efforts on behalf of Fulham Football Club over the past three seasons and, in particular, since my becoming chairman earlier this year.
"Martin was very gracious and I appreciate his understanding of the situation. There is no question Martin is an excellent football man and he has my utmost respect for the commitment he made to our club.
"However, our poor form and results this season are undeniable, and Fulham supporters deserve better. With more than half the season still ahead, an immediate change was necessary."