Giggs is the longest-serving and most decorated player in the club's history and announces his departure following the appointment of manager Jose Mourinho.
The 42-year-old announced his retirement in 2014 after a 24-year playing career, winning 23 major titles along the way, and was immediately appointed assistant manger to departed boss Louis van Gaal.
Morinho's right-hand man Rui Faria has since taken over the position, forcing Giggs to ponder demotion. However, the former Welsh international has expressed his desire to move on in order to persue his ambitions of becoming a manager elsewhere.
"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. I'll take away so many special memories as well as a lifetime of experiences that will, I hope, serve me well in the future.
"However, the time feels right and, although I have no immediate plans to step into management, it is where I want to be.
"I’ve been extremely fortunate in having two great managerial mentors; first in Sir Alex, who I’ve spent the majority of my life working with and learning from and who I believe will remain as football’s greatest-ever manager and in more recent times, Louis van Gaal, whose CV speaks for itself. The knowledge I have gleaned from them has been invaluable.
"I want to reiterate my thanks to the backroom staff and support teams at Manchester United I’ve worked with over the years. The results on the pitch are a reflection of the hard work off it. I would not have achieved the success I have without the dedication, sacrifice and commitment of these people in creating the best environment for the team to succeed.
"I want to congratulate José Mourinho on his appointment as manager of the world’s biggest club. There are only a handful of proven winners at the very highest level and José is unquestionably one of them. I know the fans will welcome him.
"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. The support you have always shown me has been phenomenal; thank you.
"It’s time for a new chapter and a new challenge. I’m excited about the future - I’ve had the best apprenticeship into management anyone could ever ask for."
Executive vice-chairman Ed Woodward added: "Ryan’s place in the history of Manchester United is assured. 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. The experiences and discipline he developed at United will undoubtedly be a big help as he continues to learn his trade. He has all the attributes to be a terrific manager in the future. Everyone at the club wishes him well in his new career. He will be missed but will always be welcome at Manchester United."