"It was a privilege to manage Fulham, one of the great clubs in the Premier League or anywhere in the world," he said.
"I am disappointed in this season but know there are better days ahead for Fulham and its supporters. I will always treasure my experience here and want to thank Mr Khan and everyone at Fulham for the opportunity."
Meulensteen, who takes charge of a Fulham team that has won only three of their 13 Premier League games and lie 18th in the league, will take charge of his first game when the Cottagers host Tottenham on Wednesday.
The Dutchman said: "I appreciate the faith Mr. Khan has put in me and will do my very best to honour his trust.
"We aim to get Fulham back on track, starting Wednesday night."
