The 29-year-old former midfielder, who retired from playing in 2018 after suffering a fractured skull, has been working with the club's academy.
He took first-team training on Monday after Mourinho's departure.
His second game in charge will be Sunday's Carabao Cup final against Manchester City at Wembley.
The club also confirmed that Chris Powell and Nigel Gibbs will be interim assistant head coaches, with Michel Vorm as interim goalkeeping coach while Ledley King will continue in his role as first-team assistant.
Chairman Daniel Levy said: "We have great belief in this squad of talented players. We have a cup final and six Premier League games ahead of us and we shall now focus all our energies on achieving a strong finish to the season."