He was dismissed at a meeting with executive vice-chairman Ed Woodward at the club's Carrington training ground shortly after 0800 BST.
Moyes, 50, was chosen by Ferguson as the man to succeed him when he retired after 26 years in charge last summer.
Player-coach Ryan Giggs is expected to take charge of United's next game at home against Norwich on Saturday.
The BBC understands coaches Steve Round and Jimmy Lumsden have also left their posts, but goalkeeping coach Chris Woods and first team coach Phil Neville will remain with the club for the rest of the season.
United had refused to comment on national newspaper reports on Monday that Moyes - who left Everton to sign a six-year deal with the Premier League champions - would be dismissed before the end of the season.
But in a statement on Tuesday the club said it "would like to place on record its thanks for the hard work, honesty and integrity he brought to the role".
Netherlands coach Louis Van Gaal, Borussia Dortmund boss Jurgen Klopp, Atletico Madrid's manager Diego Simeone and Paris St-Germain's Laurent Blanc have already been tipped as possible successors to Moyes.
United, who lie seventh in the table with four games remaining, are guaranteed to record their lowest points tally in the Premier League having struggled at Old Trafford in particular this season.
Under Moyes, they have lost six league games at home, been beaten in the FA Cup by Swansea at Old Trafford and were unable to prevent Sunderland knocking them out of the Capital One Cup in the semi-finals.
In March, some supporters chartered a plane to fly overhead during their Premier League game against Aston Villa trailing a banner with the words "Wrong One - Moyes Out" - a reference to the banner at Old Trafford that proclaimed Moyes to be the "Chosen One".
The Reds will miss out on Champions League football for the first time since 1995 and are in danger of missing out on European competition altogether for the first time since 1990.
United did reach the last eight of the Champions League before being knocked out by Bayern Munich and Moyes argued that their best displays had been in the competition.
But the Scot has been dogged by claims he has fallen out with members of his squad.
When midfielder Anderson joined Fiorentina on loan in January, he was quoted as saying other United players "wanted out" although he later denied it.
Rio Ferdinand and Robin van Persie also made less than complimentary comments about his management style, while Javier Hernandez and Wilfried Zaha posted cryptic quotes on Twitter.
At the weekend, Manchester-born striker Danny Welbeck was reported to be considering his future after becoming frustrated at regularly being played out of his favoured position.
Moyes left Everton after 11 seasons saying he could not turn down the opportunity to move to Old Trafford and began his job on 1 July.
However, United endured a difficult summer transfer window and failed in reported bids for Barcelona's Thiago Alcantara and Cesc Fabregas.
A double bid for Marouane Fellaini and Leighton Baines was dismissed as "derisory and insulting" by Moyes's old club Everton, although Fellaini finally joined on transfer deadline day for £27.5m.
Moyes was unhappy United were given a difficult start to the season, playing Chelsea, Liverpool and Manchester City in their first five games.
"I find it hard to believe that's the way the balls came out of the bag, that's for sure," he said.
But his reign began in style with a 2-0 victory over Wigan Athletic in the Community Shield at Wembley, followed by a 4-1 win away at Swansea City in the first league game of the season.
However, things quickly got worse with defeats at Liverpool and Manchester City, setting the tone for what would become United's worst Premier League season.
With the exception of the additional 21 games Matt Busby (manager from 1945-1969) had in charge as emergency manager following Wilf McGuinness's exit in 1970, and the 22 games when Jimmy Murphy stood in for Busby after the Munich air crash, Moyes's reign represents the third shortest in United history.
It is also the first time since 6 November 1986 that Manchester United have sacked a manager.
The Scot's 49 games in charge exceeds only the 43 matches Walter Crickmer presided over during the first of his two spells as manager, while Lal Hilditch was in charge for the shortest time, lasting just 33 games between October 1926 and April 1927.