Kleiman has gone 67-6 with three Football Championship Subdivision national championships at North Dakota State. He will succeed Hall of Fame coach Bill Snyder, who retired earlier this month.
Kansas State athletic director Gene Taylor promoted Klieman to head coach at North Dakota State while serving as AD 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."
North Dakota State said Klieman plans to stay on as Bison coach through the FCS playoffs. Top-seeded NDSU faces South Dakota State in a semifinal Friday night. The national championship game is scheduled for Jan. 5.
Klieman agreed to a six-year deal with Kansas State, paying him $2.3 million per year with a $200,000 annual raise, the Big 12 school said.
Kansas State chose Klieman over Troy coach Neal Brown, whose candidacy gained momentum in recent days. Memphis coach Mike Norvell and Oregon defensive coordinator Jim Leavitt, a former Kansas State assistant, also spoke with the school about its vacancy.
Klieman, 51, will return to the FBS for the first time since 1997, when he coached defensive backs at Kansas. He spent one season as head coach at Division III Loras College in 2005 before working as an assistant at Northern Iowa.
At North Dakota State, Klieman was part of a program that won six FCS titles in seven years. He was defensive backs coach in 2011, then defensive coordinator the next two seasons. He was elevated to head coach in 2014 after Craig Bohl left for the top job at Wyoming and won more national titles in 2014, 2015 and 2017.
"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," 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."
The Wildcats are following the path of Ohio State and Stanford, which hired coaches from the FCS to run their programs. Jim Harbaugh took the Cardinal to the Orange Bowl in 2010, and Jim Tressel coached the Buckeyes to the 2001 national championship.
Snyder announced his retirement Dec. 2. The 79-year-old went 215-117-1 in two stints at Kansas State, transforming the program into a consistent winner.
"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."
Kansas State was the last remaining open head-coaching job in the Power 5 conferences.