Manchester United are expected to release an official statement in the coming days.
The Welshman spent 29 years at the club as a player, coach and assistant manager and is the most decorated British player in history.
Giggs, who is now disappointed with the way United have been run since Sir Alex Ferguson’s retirement three years ago, has decided to leave the club.
Also, the former Wales international has decided to leave Old Trafford after being told he would not become assistant boss to new manager Jose Mourinho.
Giggs, 42, had a year remaining on his contract as assistant manager but new boss Jose Mourinho intends to fill that role with long-time friend, Rui Faria.
The Portuguese was always insistent he wanted to bring in his own men as he attempts to narrow the gap between themselves and the Premier League’s top dogs.
Giggs has been linked with both Bolton and Nottingham Forest vacancies in recent weeks and is understood to have spoken to at least one of them.
Steve Round, former assistant manager at the club told Sky Sports’ News:
“It’s now his opportunity to step out from Manchester United and go and be a manager in his own right.
“He can take the helm at another club, work on his leadership and build on his managerial experience.
“If he can be a success, and I really hope he can, who’s to say in five or six years’ time he can’t come back to Manchester United as an experienced manager who can take them forward post-Jose?”
During his time at the club Giggs won 13 league titles, two European Cups, four FA Cups and four League Cups.