The Republic of Ireland international has not been offered a new deal with The Black Cats and will officially become a Leicester player on July 1st, the day after his present deal at The Stadium of Light expires.
"Jason is a player who has operated at the top level and brings a wealth of experience to the club," manager Micky Adams told the official Leicester City website.
"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."