The Colts decided to offer the job to McDaniels after meeting Friday with the New England Patriots offensive coordinator to discuss shared long-term visions, sources told Schefter.
The missing element from the first meeting between the two sides was Colts owner Jim Irsay, who made the trip to New England with general manager Chris Ballard to participate in the second interview, league sources told ESPN's Chris Mortensen.
The NFL Network reported earlier this month that McDaniels was expected to accept the Colts' offer.
McDaniels, 41, will inherit a Colts team that went 4-12 and finished last in the AFC South in 2017 under Chuck Pagano.
The Colts own the No. 3 overall pick in this year's NFL draft and expect to have franchise quarterback Andrew Luck, who missed the entire 2017 season because of a shoulder injury, healthy for the 2018 season.
This will mark McDaniels' second stint as a head coach. He led the Denver Broncos to an 11-17 record before being fired midway through the 2010 season.
McDaniels has been one of the league's most coveted coordinators since returning to New England in 2012. Since then, the Patriots have reached six consecutive conference championship games and won two Super Bowls.
With McDaniels' exit to Indianapolis, the Patriots are expected to lose both coordinators to head-coaching jobs, as defensive coordinator Matt Patricia will become the Detroit Lions' head coach, sources told ESPN earlier this month. New England also has respected special teams coordinator Joe Judge on an expiring contract.