Kleiman will sign a six-year contract worth $2.3 million per season, sources told Jake Trotter of ESPN.
"I'm very excited to have Chris Klieman lead our program," Kansas State athletic director Gene Taylor said. "He is a perfect fit for us, both from a personal standpoint and as a head coach.
"He's a tremendous teacher who I had the pleasure to hire at NDSU and watched him turn into a very successful coach. He will bring a ton of energy and excitement. His teams play extremely hard, disciplined football. He's a winner. That's all he does is win, and we're excited to have Chris, Rhonda and the entire Klieman family join our K-State family."
The 51-year-old is expected to continue to coach NDSU through the FCS playoffs before leaving to succeed Bill Snyder, who retired after 27 years with the program.
Kleiman will leave the Bison with an incredible record of 67-6 and three national titles.
Taylor previously worked with Kleiman at NDSU and promoted him to head coach after Craig Bohl left for Wyoming in 2013.