The 36-year-old was Moyes's captain at Everton and is expected to be part of a major influx from Goodison Park including Steve Round, Chris Woods and Robbie Cooke.
Neville, who played 386 games for United before joining Everton in 2005, is expected to become first team coach.
The appointment comes as a shock move with Neville replacing the hugely respected Rene Meulensteen, who has reportedly chosen to quit Old Trafford rather than accept a demotion to become youth team coach.
Last month Neville confirmed he would leave Everton at the end of the season. He holds a UEFA B coaching licence and is part of Stuart Pearce's England Under-21 staff.
Moyes has already dispensed with the services of Sir Alex Ferguson's assistant Mike Phelan and goalkeeping coach Eric Steele, while chief scout Martin Ferguson - Sir Alex's brother - has also left.
The highly-rated Meulensteen has been at Old Trafford since 2001, excepting a six-month period in 2006 when he became manager of Danish side Brondby.
He has been working with the first team since 2007 and was a key member of the coaching staff for four Premier League titles, two League Cups and a Champions League victory.
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- Rene Meulensteen