United have turned to the club's record appearance holder to fill the void created by Moyes' departure earlier on Tuesday.
The 40-year-old, who was player-coach under Moyes, will be in charge at Old Trafford until a permanent replacement is appointed.
The club said in a statement: "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."
Giggs will take charge for the first time for this weekend's home clash with Norwich, which you can see live on Sky Sports 1.
The Welshman is among the contenders to become a permanent replacement for Moyes with Holland coach Louis van Gaal Sky Bet's favourite to get the job.
The appointment of Giggs to replace Moyes has won universal backing from his former United team-mates Dwight Yorke and David May.
May told Sky Sports News Radio that Giggs will be a perfect appointment to take the reins.
Yorke admits he would have given the job to Giggs last summer prior to the appointment of Moyes.
"I would have given Ryan Giggs the job last summer because there would have been a continuation there," Yorke told Sky Sports News.
"He has been at the club for over 20 years, he's a true Red and of course he's doing his Pro licence. Yes, people always question whether he has got the experience but Sir Alex would have been there to guide him and he would have been able to keep the backroom staff."
Sky Sports expert Jamie Carragher also feels Giggs will be a safe pair of hands to take charge of first-team affairs, but believes Borussia Dortmund's Jurgen Klopp would be the ideal candidate to take over at Old Trafford.
Carragher said: "This is new for Ryan Giggs but he knows the Manchester United way of doing things and he's taking his coaching badges so he obviously wants to be a manager.
"He knows the club inside out and if he has a great end to the season, who knows?
"I'd imagine they'd bring another manager in though and keep Giggs as part of the coaching staff.
"Louis van Gaal is the elder statesman, the experienced man and maybe the man with the ego to take on Manchester United but he'll be with Holland at the World Cup and United want to get on with transfers.
"Jurgen Klopp, full of energy and personality, would be a better fit. A new manager needs to inject power and pace into this Manchester United side."
However, United could face a fight to land Klopp with the German insisting he has no plans to quit Borussia Dortmund.
Sky Sports 1 will broadcast a special programme - Moyes: Story of the Day - from 7pm looking back at how the Manchester United manager's sacking unfolded on Sky Sports News with reaction, analysis and a look at the contenders to take over. This will be followed at 10pm on SS1 and Sky Sports News by Manchester United: The Verdict, analysing United's decision to replace Moyes.