The 54-year-old takes over from Paul Hart in the Eagles hot-seat, with Palace legend Dougie Freedman named as Burley's number two.
Burley has previously enjoyed spells in charge of Ayr United, Colchester United, Derby County, Hearts and Southampton alongside his time at Portman Road.
Most recently he was head coach of the Scotland national team, but was sacked in November last year following a 3-0 friendly defeat by Wales.
Palace escaped relegation from the Championship on the final day of last season, drawing 2-2 at Sheffield Wednesday to send the Owls down.
Earlier on in the campaign they had been docked ten points by the Football league for going into administration.