The team scheduled a Tuesday afternoon news conference to introduce McCoy, who had been the offensive coordinator for the Denver Broncos.
The 40-year-old McCoy replaces Norv Turner, who was fired along with general manager A.J. Smith after the Chargers finished 7-9 and missed the playoffs for the third straight season.
McCoy's hiring comes three days after the top-seeded Broncos were eliminated from the playoffs in a home loss to the Baltimore Ravens.
The coaching search was led by Tom Telesco, who was hired as Chargers GM last week. Telesco also is 40.
The Broncos have won consecutive AFC West titles. McCoy tutored quarterbacks Kyle Orton and Tim Tebow in 2011, and Peyton Manning in 2012.
McCoy, who interviewed with the Miami Dolphins last year after retooling Denver's offense to fit Tebow's skill set, burnished his head coaching credentials this season while blending the power formations the Broncos used in leading the league in rushing last year with Tebow and some of the spread formations that Manning ran in Indianapolis.
"I think he's going to be a great head coach. Very detail-oriented, knows the game, relates with players very well," Broncos wide receiver Brandon Stokley said. "So, I think he'll be an excellent head coach."
Denver swept the Chargers in 2012, including an epic 35-24 victory at San Diego on Oct. 15 when Manning calmly led them 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.
McCoy played quarterback at Long Beach State and Utah before moving on to the NFL Europe and the CFL. He began his pro coaching career with Carolina in 1999 before moving to the Broncos in 2009.
McCoy was rumored to be a leading candidate for the Cardinals job. The Cardinals interviewed him during the Broncos' bye week and were hoping to bring him in Tuesday for a second interview.
With McCoy out of the running, speculation now focuses on defensive coordinator Ray Horton, who has already interviewed twice with Cardinals president Michael Bidwill.
Cincinnati offensive coordinator Jay Gruden interviewed with Arizona last week, and there have been conflicting reports on whether the Cardinals interviewed Steelers offensive coordinator Todd Haley. There are no other known candidates for the Arizona opening, and with Steve Keim on board as the team's general manager, it would seem likely that a decision could come soon.