United legend Giggs, who was part of Moyes' backroom staff in a player-coach capacity, will oversee United's first-team affairs on a temporary basis until a permanent successor is found.
A club statement read: "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."
Moyes' reign at Old Trafford came to an end less than 12 months into his six-year contract following Sunday's 2-0 defeat at the Scot's former club Everton, a result that guaranteed reigning English champions United cannot qualify for next season's UEFA Champions League.
His departure was announced via the club's official Twitter account, with United thanking Moyes for his "hard work, honesty and integrity" during his short tenure.
United sit seventh in the Premier League with four matches remaining, 23 points adrift of leaders Liverpool.
