The former Huddersfield, Birmingham and Blackpool boss was at Rugby Park on Monday morning for a media conference.
Lee McCulloch has led the side since Gary Locke resigned on January 30, winning at Motherwell on Saturday after earning a William Hill Scottish Cup replay with Rangers.
That replay, on Tuesday, will be the new manager’s first game in charge.
McCulloch, who is being retained as an assistant, said: “I believe the board has made a fantastic appointment having taken time to interview a number of strong candidates and I look forward to introducing him to the media.
“With everyone pulling together, I’m confident that the new manager will lead the team to success. On a personal note, I have thoroughly enjoyed being interim manager and thank the board, staff, players and fans for their support and encouragement.”
Clark, 43, most recently managed Blackpool where he won three of 33 games in charge, although he had considerably more success in his first job at Huddersfield where he won 87 of 178 games at the helm.
Kilmarnock sit 10th in the Ladbrokes Premiership, a point above second-bottom Motherwell.