The 33-year-old, who was released by Sunderland at the end of the season, has agreed an initial 12-month deal at The Walkers Stadium.
The Foxes have already agreed deals for Gareth Williams and Danny Tiatto as they look to bounce back to The Premiership at the first time of asking.
"Jason is a player who has operated at the top level and brings a wealth of experience to the club," said Foxes boss Micky Adams.
"He is an excellent player and we have had to beat off many other clubs for his signature.
"With the arrival of Gareth Williams and Danny Tiatto it means we have significantly strengthened our midfield. There will be several more new faces yet elsewhere into the squad and our search continues."
