The former Blackpool boss has signed a three-and-a-half year deal after replacing Beale, who joined Rangers last month.
Critchley had previously succeeded Beale as assistant manager at Aston Villa in the summer, after Beale moved to Loftus Road, but was out of work following the sacking of Steven Gerrard in October.
“I am very excited and can’t wait to get started,” Critchley told the club’s official site, having been appointed following QPR’s 3-0 home defeat to Burnley on Sunday which left them ninth in the Sky Bet Championship.
“It is a huge honour for me and I would like to thank the owners, Les Ferdinand and Lee Hoos for entrusting me to lead the club.
“I would also like to thank Paul Hall and his staff for the hard work they have put in during the interim period.
“Now I am looking forward to getting to work with the players and staff. I already know some of the players from working with them previously and I am aware of a number of them, having followed their careers from afar.
“There have been some good foundations laid here and now it is my job to work as hard as I can to build on that.
“We want to move the club forward and ensure we are competing at the top end of the Championship table.”