The 49-year-old Dutchman has departed following new manager David Moyes' decision to bring in his own backroom staff.
Executive vice-chairman Ed Woodward said on the club's website: "I'd like to thank Rene for his contribution to the club.
"He has been first-team coach for five years and in that time has given great assistance to [former manager] Sir Alex Ferguson and [former assistant manager] Mick Phelan in keeping the team at the top of the game not only in this country but in Europe as well."
Meulensteen thanked the club's owners, his colleagues, the players and fans "who made my time at Manchester United very special and one I will never forget."
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