Martin Jol paid the price for six consecutive defeats on Sunday afternoon when he was fired after two-and-a-half years at the club.
Meulensteen had two spells on Sir Alex Ferguson's backroom staff and the Scot described the 49-year-old as a "magnificent coach" in his autobiography.
Meulensteen's previous experience as a number one is very limited, however.
He lasted just 17 days at Anzhi Makhachkala and his previous management roles came at Brondby and Qatari teams Al-Gharafa and Al-Sadd.
Former Brondby player Per Nielsen criticised Meulensteen in his recently published autobiography, claiming the Dutchman alienated some players with his tactics and training routines.
Meulensteen, who is understood to have a contract until the end of the current season, concedes being in charge of a struggling team like Fulham will be difficult after spending 12 years at Manchester United, but he insists he is up to the challenge.
"I am confident because of the sort of experiences I've had for so many years at Manchester United," Meulensteen told Sky Sports News.
"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."
The sorry performance that Fulham delivered during Jol's final game in charge summed up just how big a task Meulensteen has ahead of him.
The Cottagers were static at the back, they were slow in midfield and lacked any kind of attacking conviction in what was a truly demoralising 3-0 defeat at West Ham.
They sit three points from safety and have a tricky home fixture against Tottenham coming up on Wednesday.
"It's a massive challenge," Meulensteen added.
"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."
Jol and Meulensteen have spoken since Fulham owner Shahid 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 (Jol's departure) was anything to do with me, but it was definitely not something I was anticipating.
"We wanted to turn this corner together."
Fulham forward Bryan Ruiz used his official website to thank Jol for bringing him to Craven Cottage while throwing his support behind the new boss.
"I am very grateful to Martin because he was responsible for bringing me to Fulham, I learned a lot from him," Ruiz said.
"He came to my defence. I always tried to do my best to back him."
On Meulensteen's appointment, he added: "It's a change that we hope will help the team. We as players are going to give our best."
Source: PA
Source: PA