Giggs, 40, has been combining playing with studying for his Pro-Licence, learning at the feet of the manager for the majority of his career at United, Sir Alex Fergsuon.
The Welsh winger and Moyes are believed not to have seen eye to eye over the past season although the club was at pains to deny the rumour.
United released a short statement at 8.30am on Tuesday morning saying: “Manchester United has announced that David Moyes has left the club. The club would like to place on record its thanks for the hard work, honesty and integrity he brought to the role.”
Giggs will now be in charge for the last four games of the season, beginning with Norwich at home in the 5.30pm kick-off on Saturday, followed by home games against Sunderland and Hull and finishing away to Southampton.
Moyes drove into the club’s Carrington training complex on Tuesday morning for a meeting with the chief executive Ed Woodward to make his departure official. Moyes’s backroom staff of Steve Round, Jimmy Lumsden and Chris Woods are also likely to depart although Phil Neville may be kept on.
The move, revealed in The Guardian on Monday, came after the former Everton manager lost the support of United’s owners, the Glazer family despite having been personally selected by Ferguson and been handed a six-year contract.
United had insisted that Moyes was still their manager on Monday, but refused to deny widespread reports the Scot was to be dismissed.
The former captain Gary Neville, who made over 600 appearances for United, had called on the club to clear up the situation.
“I have to say I find it repulsive the way these rumours break,” Neville, who won 17 major trophies at Old Trafford, told Sky Sports. “I don’t like it, I’ll never get used to it, even though this is the world we live in. It needs to be clarified pretty quickly by the club and they need to break rank and do what they don’t usually do, which is make a statement pretty quickly.
“The weight and explosion of the information coming out concerns me. That club, for 20-odd years, contained and managed information. It was completely off the scale like nothing else that’s happened at the club in 20 years.”
Managers are already being linked with the job, foremost among them the Holland manager Louis van Gaal and the former United centre-half and Paris St-Germain coach Laurent Blanc.
Carlo Ancelotti, who has also been touted as a possible successor to Moyes, was non-committal ahead of Real Madrid’s Champions League semi-final meeting with Bayern Munich.
“I feel sorry for David Moyes, but that’s the life of a football coach, sometimes it doesn’t go well for you and you are sacked,” he said.
“I’m sure Moyes is going to get another team and another opportunity, but I always feel bad when a coach is sacked. I am a little surprised because Manchester United don’t normally do this.”
The Bayern Munich coach Pep Guardiola, who is preparing his team for Wednesday night’s meeting with Real in the Champions League semi-finals, said: “I’m here. I’m comfortable. I want to stay two more years at Bayern.”
The club’s press officer added: “Tell the people in England there is no chance.”
The United players started leaving Carrington at around 1.30pm, but there was no sign of Moyes, who was thought to have left the site via a back exit away from the cameras.
The coach Nicky Butt, who is expected to form part of Giggs’ interim backroom staff, left via the main exit shortly after 2pm.
The list of unwanted records broken during Moyes’ time at the helm is as embarrassing as it is long. United will end the season with their lowest points total in Premier League history, they have not qualified for the Champions League for the first time in almost two decades and their home record this season is the worst since 1978.
The Red Devils, who won the title by 11 points under Sir Alex Ferguson last year, are seventh in the Premier League with four matches left. During his tenure Moyes won 27, drew nine and lost 15 of his 51 games in charge.
Had he not made a mess of the summer transfer window, he might have been better placed. The Scot pursued Barcelona’s Cesc Fábregas when the Spaniard had no intention of leaving the Spanish club. Thiago Alcântara joined Bayern Munich ahead of United, while the club made a hash of their attempts to sign Marouane Fellaini and Leighton Baines , their bid of £28m for the pair being branded “derisory and insulting” by Everton.
Baines stayed and United ended up buying Fellaini for £27.5m when they could have bought him for £4m less had they acted quicker.