The move was first reported by NFL Network's Jason La Canfora. Crennel and the team agreed to a three-year contract late Sunday night, according to his agent, Joe Linta.
"The three games had a lot to do with where we arrived at this decision," Chiefs general manager Scott Pioli said. "Some of the things we saw was a great deal of accountability and consistency. There was also a different energy to the football team. A lot of it had to do with those last three games."
Crennel always was considered the front-runner to replace Haley, even though Pioli said he interviewed "more than half a dozen" candidates for the job. Linta, who also represents four Chiefs players, said his clients are "ecstatic" about the move.
"I'm not exactly sure what a player's coach is," Crennel said. "Sometimes I think players think that a coach who is on their side is a player's coach, who always rules in favor of them may be a player's coach. I know that's not always the case with me. I think that basically, I'm a good guy. And I think this is what players appreciate -- players appreciate honesty. Players appreciate you telling them like it is. They don't always want to hear it. But that's what they appreciate. I try to tell them what I believe, what I feel and how I think it should be done."
The Chiefs have a big decision to make at quarterback, where veteran Kyle Orton finished the season for Matt Cassel, who was out most of the second half of the season with a hand injury. Crennel also was noncommittal when asked about his staff, but he did leave the door open that he could be his own defensive coordinator.
La Canfora reported that Crennel is working with team management to identify an offensive coordinator. First-year offensive coordinator Bill Muir came under criticism even though the unit was greatly weakened by season-ending injuries at the beginning of the year to tight end Tony Moeaki and Pro Bowl running back Jamaal Charles.
"One thing (Crennel) said at the time was, 'I want you to go out and talk to other people because if you make this decision, I want you to know that you're making the right decision,' " Pioli said.
The Associated Press contributed to this report.