"Mr Khalifa was refused leave to appeal to the Supreme Court on December 3. He will be extradited within 28 days of that date," said a spokesperson for the Home Office.
Once considered the "golden boy" of Algeria, Khalifa came from obscurity to build an empire including a bank, an airline and television stations, and employed 20,000 people in Algeria and Europe.
He took refuge in Britain in 2003 when his business collapsed, costing the Algerian state and individual savers between USD 1.5 billion and $5 billion (1.1 billion and 3.6 billion euros).
He is to go into an appeal hearing on his return to Algeria.
French authorities are also seeking to extradite Khalifa on fraud and embezzlement charges, but the Algerian request takes precedence.