Klieman guided the Bison to a 67-6 mark overall with three Football Championship Subdivision national championships during a four-year stretch. He will succeed Hall of Fame coach Bill Snyder, who retired earlier this month.
The 51-year-old Klieman agreed to a six-year deal with Kansas State, paying him $2.3 million per year with a $200,000 annual raise over the remaining five years of the contract, the Big 12 school said.
"This is an absolute dream job," Klieman said in a statement. "I'm so happy and thrilled to follow a legend in Coach Snyder. I've followed him from afar, went to his camps while playing in Waterloo, Iowa, and played against his Kansas State team when I was at Northern Iowa. The opportunity to follow in an icon's footsteps is something I don't take for granted and don't take lightly.
"I know I have huge shoes to fill, and I'm excited to carry on his legacy. I have prepared my entire life for this opportunity and had great experiences at many institutions, most notably North Dakota State where we've had unmatched success over the last eight years. I can't express how pleased I am and thank President Myers, (athletic director) Gene Taylor and the search committee for trusting in me and handing over the keys to this great program."
Snyder posted a 215-117-1 record over 27 seasons at Kansas State with a pair of Big 12 conference championships and five division titles. The 79-year-old became the fourth active coach to be enshrined in the College Football Hall of Fame in 2015.
The Wildcats finished just 5-7 in 2018, marking Snyder's first losing season in 13 years.
Klieman has ties to Kansas State, as Taylor promoted him to head coach at North Dakota State while serving in the same role at the school in 2013.
"I'm very excited to have Chris Klieman lead our program," 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."
Klieman plans to remain with the top-seeded Bison (13-0) heading into the FCS playoffs. The team faces South Dakota State in a semifinal on Friday.
"I want to congratulate Coach Klieman and sincerely thank him for the impact he's had these past five years on the NDSU football program, our players, the Fargo community and Bison Nation," North Dakota State athletic director Matt Larsen said in a statement. "Aside from the incredible success on the field, his players consistently excelled at a high level in the classroom and willingly gave back to the community. He has always honored and preserved the traditions and culture of excellence surrounding Bison football, and for that I am forever grateful."