Meulensteen, a former first-team coach at United under Sir Alex Ferguson until the Scot retired in May, was appointed Cottagers boss on Sunday night after Martin Jol was sacked.
Fulham have confirmed that Jol's brother Cornelis, who worked as football operations manager, plus coaches Michael Lindeman and Billy McKinlay have also left the club. Kit Symons, who is the current development team manager, will also be assisting with first-team training.
Jol paid the price for six consecutive defeats when he was fired after two-and-a-half years at the club, and with Fulham 18th in the league table.
Fulham said in a statement: "Fulham Football Club would like to welcome Jonathan Hill, appointed as first-team coach to work with Rene Meulensteen.
"Jonathan Hill worked at Manchester United for 10 years as academy youth coach prior to joining the Jordanian Football Association as technical director in 2009 where he was responsible for all of the national youth teams from Under-8s to Under-20s. More recently, Jonathan has coached at both Manchester City and Tromso FC.
"Michael Lindeman, Billy McKinlay and Cornelis Jol have left the club and we would like to thank them for their service and wish them well for the future."