His dismissal was announced shortly after 0830 BST, following a meeting with executive vice-chairman Ed Woodward at the club’s training ground.
Moyes, 50, was chosen by Ferguson to succeed him when he retired after 26 years in charge last summer.
United said player-coach Ryan Giggs will take charge “until a permanent appointment can be made”.
His first match as interim boss will be the home game 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 shares, which trade on the New York Stock Exchange, were up more than 6.5 per cent at $18.80 at 1830 BST, signalling investor relief at the decision to sack Moyes.
On Monday, United had refused to comment on newspaper reports that Moyes, who left Everton to sign a six-year deal with the Premier League champions, would be sacked before the end of the season.
However, those reports prompted club officials to hold talks with the Scot late on Monday in a move designed to prevent a drawn-out dismissal process.
In a short statement on Tuesday, the club said Moyes had departed, adding 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 been tipped as possible successors.
However, Klopp has ruled himself out of the job, the 46-year-old telling The Guardian: “Man Utd 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.”
Former Manchester United and England striker Michael Owen said on Twitter: “Huge news at Old Trafford but with the summer looming and a huge transfer kitty available United had to be 100% Moyes was the right man.
“Evidently they didn’t have the confidence in him in which case makes the timing absolutely right. Now the big question is who’s next?”
The Daily Telegraph suggest United will make discreet moves to see if Pep Guardiola can be persuaded to leave Bayern Munich.
But BBC Sport has learned that Giggs is not under consideration for the role on a full-time basis.
“I definitely think Ryan will be a manager,” said former United captain Bryan Robson. “Whether he gets it full-time at a club like Manchester United is a big ask.”
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 defeating them in the Capital One Cup 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 Red Devils 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 reached 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 Serie A side Fiorentina on loan in January, he was quoted as saying other United players “wanted out” although he later denied it.