32-year-old Blake will be a direct replacement for the injured Brian Deane, out for six weeks because of a shoulder injury.
Blake, who has been capped 29 times by Wales, cost Blackburn £4.25m back in October 1998 when he joined from Bolton Wanderers.
He joined Leicester from Wolves in a free transfer this summer but has scored only one goal for the Foxes. The forward has made just five starts this season, his last one being earlier this month, and has made ten other appearances as a substitute.
Blake goes straight into the squad for the New Year's Day game against Crewe Alexandra and has been given squad number 21.
Meanwhile, Leeds have sent winger John Oster back to Sunderland.
An internal inquiry at Leeds found the 26-year-old had breached the club's discipline after an incident at the club's Christmas party.