McCoy has been the Denver Broncos offensive coordinator since 2009, helping the Broncos reach the AFC divisional playoffs in each of the last two seasons.
McCoy becomes the second Broncos coordinator to take a head coaching job within the AFC West in two seasons. Last offseason, former Broncos defensive coordinator Dennis Allen was named coach of the Raiders.
New general manager Tom Telesco has led the search for a coach to replace Norv Turner, who was fired along with GM A.J. Smith on Dec. 31 after the Chargers finished 7-9.
Before his Chargers interview, McCoy already had interviewed with Arizona, Philadelphia and Chicago. The Jaguars also were expected to talk with him.
McCoy was a quarterback at Utah from 1992-1994, leading the Utes to a dramatic 16-13 win over Arizona in the 1994 Freedom Bowl. McCoy threw a 5-yard touchdown to Kevin Dyson in the final minute for the victory.
McCoy, 40, interviewed with the Dolphins last season before being passed over in favor of Joe Philbin, the former offensive coordinator of the Packers.
McCoy also drew praise for helping the Broncos reach the playoffs last season with a read-option offense run by Tim Tebow. McCoy has been the Broncos' offensive coordinator since 2009.
Denver swept the Chargers in 2012, including an epic 35-24 victory at San Diego on Oct. 15, when Peyton Manning led the Broncos back from a 24-0 halftime deficit.
With the Chargers, McCoy will work with Philip Rivers, who struggled this season, in large part because of a shaky offensive line. Rivers was sacked 49 times and committed 22 turnovers, giving him 47 turnovers in two seasons.