Kansas officials said Weis would be introduced at a Friday news conference.
Weis, 55, spent five seasons as head coach at Notre Dame. He also has been an assistant coach for three NFL teams and was offensive coordinator with the Florida Gators in 2011.
He will replace Turner Gill, who was fired after compiling a 5-19 record in his two seasons at Kansas. Gill had three years remaining on a $10 million contract.
Weis went 35-27 during his stay at Notre Dame. The Irish made it to a BCS bowl appearance in each of his first two years at the school, but went 16-21 during the next three seasons.
He was fired after a 6-6 record in 2009.
Before going to Notre Dame, Weis was best known for his work with New England quarterback Tom Brady, who began his NFL career as a sixth-round draft pick and has gone on to be the MVP in two Super Bowls.
Weis also worked under Bill Parcells with the New York Jets from 1997 to 1999.