Crist posted the news on his Twitter account Thursday, saying, "After a long & difficult decision making process, I'm incredibly excited to join the Kansas football team."
Crist began this season as the Irish's starter, but was replaced by Tommy Rees after one half of play in Notre Dame's season-opener against South Florida.
Weis was the Irish's head coach for Crist's first two years in the program, but was fired after a 6-6 season in 2009. He was named Kansas' head coach earlier this month.
Crist's most productive season at Notre Dame was his junior season in 2010. He completed more than 59 percent of his passes for 2,033 yards and 15 touchdowns, but suffered a ruptured patella tendon in the ninth game of that season.