Burley, 54, was chosen for the role ahead of Paul Hart and Chris Coleman by the CPFC 2010 consortium who took over the club last week. He will be assisted by Dougie Freedman.
Hart had been in charge at the end of last season as the Eagles avoided relegation to League One with a draw at Sheffield Wednesday on the final day of the season.
Burley will be remembered best for taking Ipswich Town into the Uefa Cup in 2001, but also had spells in charge of Derby County, Hearts and Southampton.
He was sacked as Scotland manager in November after failure to qualify for the World Cup finals.
Palace head to Glanford Park on Saturday August 28, while they host the Iron at Selhurst Park on Saturday April 16.