The 42-year-Welshman played 963 games for United, winning 13 Premier League titles and two Champions Leagues in a glittering career before hanging up his boots in 2014.
He worked in coaching roles with managers David Moyes and Louis van Gaal after Alex Ferguson retired in 2013 but decided not to seek a role alongside Jose Mourinho who took over the top job in May.
"After 29 seasons at Manchester United as a player and assistant manager, I know winning is in the DNA of this club - giving youth a chance, and playing attacking and exciting football," Giggs said in a club statement.
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"It’s healthy to have high expectations, it’s right to expect to win. Manchester United expects, deserves, nothing less," he added.
“This is why it is a huge decision for me to step away from the club that has been my life since the age of 14. It has not been a decision that I have made lightly.
“However, the time feels right and although I have no immediate plans to step into management, it is where I want to be."
Giggs congratulated Portuguese Mourinho on his appointment.
"There are only a handful of proven winners at the very highest level and Jose is unquestionably one of them," he said.
"My final thank you is to the fans. I cannot begin to tell you how much I will miss walking out at Old Trafford in front of you. It’s extremely difficult to say goodbye after 29 years. I have loved every minute both as a player and assistant manager.
United Executive Vice Chairman Ed Woodward paid tribute to Giggs's contribution.
“Ryan’s place in the history of Manchester United is assured," he said.
"He has been a constant presence at the club since 1987 and during his playing days, regularly delighted crowds; first with his dazzling wing play and later with his intelligence and ability to dictate a game."
"He has tackled his coaching and management responsibilities with similar rigour and diligence. Everyone at the club wishes him well in his new career."
(Reporting by Ed Osmond,; Editing by Neville Dalton)
