Team officials used their Twitter account to make the announcement, posting a photograph of Reid signing his contract with team Chief Executive Officer Clark Hunt at his side.
The deal is reportedly for five years.
Reid, 55, was fired as head coach by the Philadelphia Eagles Monday, becoming one of seven NFL coaches to be dismissed since the regular season ended last Sunday.
Romeo Crennel, who Reid will succeed in Kansas City, also was fired Monday.
Reid coached the Eagles for 14 years, during which they reached the NFC title game five times. They won only one of those games, however, and then lost to New England in the Super Bowl at the end of the 2004 season.
His 130 regular-season wins with the Eagles are the most for a coach in franchise history.
Reid's hiring came after the Chiefs dismissed General Manager Scott Pioli earlier in the day. Pioli had been with the team for four years.
That clears the way for Reid to become chief of football operations, which allows him to hire a general manager of his choosing.
Earlier in the week, there had been speculation Reid was headed for the Arizona Cardinals, which had him at the top of their list as a replacement for Ken Whisenhunt. Reid, however, agreed to terms with Kansas City before he interviewed with the Cardinals.
Philadelphia went 4-12 this season while the Chiefs were only 2-14. Kansas City owns the No. 1 pick in this year's draft.