Giggs, 39, signed a one-year extension with United in March but has been taking his coaching badges and is due to attain the Uefa Pro Licence next summer.
"It's a great privilege to be appointed a player/coach," Giggs said. "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. It's no secret that I have been taking my 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."
Moyes added Giggs was "an example to any aspiring young player" and lauded his "ability to adapt his game over a number of years".
Giggs will be joined by former teammate Phil Neville on Moyes' backroom staff.
Steve Round, Jimmy Lumsden and Chris Woods have all followed Moyes to Old Trafford from Everton.
United's record appearance holder, Giggs has won 13 Premier League titles, four FA Cups, three League Cups, two Champions League winners' medals, the Intercontinental Cup and the Club World Cup in his 22-and-a-half-years in the Reds' first-team.