Daboll had the same job at Cleveland in 2009-10 and at Miami last season.
The Dolphins were 20th in points scored in the NFL at 20.6 points per game but that was much better than the Chiefs, who averaged 13.2 points and were next-to-last in the NFL.
"Brian is a fine football coach and offensive mind," said Kansas City Coach Romeo Crennel.
"I worked with him when he was a young coach in New England and I am proud of the way his career has developed. We had a very thorough process for this position and it was clear to me that Brian was the right choice. He was coveted by multiple teams and I am glad he will be joining our staff."
Daboll coached at William and Mary and Michigan State before moving to the NFL as a defensive coaching assistant with New England. He was on staffs with the Patriots and New York Jets before becoming the offensive coordinator at Cleveland.