Giggs, 39, signed a one-year extension to his playing contract in March and will combine his new duties with being a member of the first-team squad.
Neville, who played for United from 1995 to 2005 and who retired after leaving Everton at the end of last season, follows his old boss David Moyes to Old Trafford.
"I'm delighted Ryan has accepted the chance to become player-coach. His success and ability to adapt his game over a number of years gives him an unrivalled perspective on the modern game," Moyes said in a statement.
"His career is an example to any aspiring young player and I'm sure both he and the players will benefit from his new role."
Former Welsh international Giggs, who made his senior debut for United in March 1991, is the most decorated player in English football with 13 Premier League winner's medals, four FA Cup winner's medals and two Champions League winner's medals among his collection.
"It's a great privilege to be appointed a player-coach. I hope I will be able to bring my experience to bear, having been both a player and part of the Manchester United family for so long," Giggs said.
"It's no secret I have been taking my [coaching] qualifications and I see this as the first step in my future career. I'm really looking forward to working alongside David and the team."
"I have known and worked with Phil for eight years and in that time I have come to know his dedication, ability to lead and appetite for hard work," he said.
"In addition, of course, he understands the club very well and I think his addition to the coaching staff will be a valuable one."
His older brother Gary, who had a one-club career with United and played 85 times for England, retired in 2011 and is a member of England coach Roy Hodgson's backroom staff.
"When I retired from football I knew that I wanted to continue in the game," Phil said.
"When David called to give me this opportunity I couldn't resist. I gave my all when I played for Everton but it is no secret that this club is in my heart."
