It emerged on Saturday the former Porto and Blackburn striker McCarthy had joined United as a striker's coach, with the South African photographed at the club's Carrington training complex.
United said McCarthy “will specialise in coaching attacking plays and positioning”.
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McCarthy, 44, is a boyhood United fan and scored both goals in Porto's 2-1 Champions League round-of-16 first leg victory over United in 2004.
Technical director Fletcher will remain on the first-team coaching staff, having been involved in training during United's pre-season tour of Thailand and Australia.
Fletcher officially returned to United as a first-team coach in January 2021 and was then named technical director in March but continued to participate in training.
The 38-year-old observed matches from the press box and the directors' box before he moved into the dugout with the rest of the first-team staff for Ole Gunnar Solskjaer's last match in charge in the defeat at Watford in November.
United explained Fletcher “also has a wider remit as technical director, overseeing the path from Academy to the first team, plus players out on loan”.
Ten Hag has already added Mitchell van der Gaag and Steve McClaren as his assistant coaches, with Eric Ramsay kept on. Richard Hartis and Craig Mawson are still the goalkeeping coaches.