It is understood Moyes was axed by vice-chairman Ed Woodward during a meeting at the club's Carrington training ground shortly after 0800 BST on Tuesday.
A club statement read: "Manchester United announces 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."
The club later confirmed Giggs would be handed the reins for the time being - United host Norwich in their next game on Saturday.
It added: "Following the departure of David Moyes as manager, Manchester United has announced that Ryan Giggs, the club’s most decorated player, will assume responsibility for the first team until a permanent appointment can be made.
"The club will make no further comment on this process until it is concluded."
The news of Moyes' exit had been widely expected after it was widely reported on Monday afternoon that the Scot was to be axed in the wake of Sunday's 2-0 defeat at his former club, Everton.
Moyes, appointed on a six-year contract only last summer, took over a team crowned champions last season.
However, a miserable campaign has seen them fail to qualify for the Champions League for the first time in almost 20 years and the Red Devils currently sit seventh in the Premier League table.
Moyes, who spent 11 years at Everton before moving to Old Trafford, always knew he had a tough act to follow with his predecessor Sir Alex Ferguson regarded as the most successful British manager of all time.
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But few could have predicted the season would go as badly as it has with United having lost 11 of their 34 league games so far. The run means are are struggling to even qualify for the Europa League.
United are guaranteed to end the season with their worst points total in Premier League history and Moyes' home record is the worst of any United boss since 1978 when Dave Sexton was in charge.
Moyes spent more than £60million on recruiting Juan Mata and Marouane Fellaini in the last two transfer windows and there have been suggestions that the club is prepared to throw another £200million at improving the squad this summer.
In the immedaite aftermath of Moyes' departure, Louis van Gaal was the bookies' favourite to become the next permanent United manager. He is currently due to lead the Netherlands at this summer's World Cup.
Sky Bet also had Borussia Dortmund's Jurgen Klopp and Atletico Madrid manager Diego Simeone towards the head of their early market.
However, Klopp, who signed a new five-year deal at Dortmund back in October, was quick to rule himself out of the running, telling The Guardian: "Man United is a great club and I feel very familiar with their wonderful fans. But my commitment to Borussia Dortmund and the people is not breakable.''
Moyes was dogged by claims he was not up to the job ever since he took over last July.