The 49-year-old Austrian replaces Roy Hodgson, who stepped down on Monday so Palace could "bring forward their plans to appoint a new manager at the end of the season".
Palace are 16th in the Premier League after 10 defeats in the past 16 games.
Glasner has signed a contract until June 2026 and will be in charge for Saturday's home game against Burnley.
He was pictured watching Tottenham's defeat by Wolves on Saturday, with Spurs hosting Palace on 2 March.
Hodgson's coaches Ray Lewington and Paddy McCarthy will be in charge of Monday's game at Everton.