McCoy, the Broncos offensive coordinator since 2008, replaces Norv Turner, who was fired at the end of the season along with General Manager A.J. Smith.
McCoy also served as an offensive assistant for the Carolina Panthers from 2000 through 2008.
"Mike has all of the qualities we were looking for in a head coach and a leader," Chargers President Dean Spanos said. "Bottom line, he's a leader. And he's charismatic. I know our fans will enjoy getting to know Mike and watching what he does with the Chargers."
The Chargers reportedly decided to go with McCoy prior to interviewing all candidates. Colts offensive coordinator Bruce Arians was due to meet with the team Wednesday.
McCoy will team up with new GM Tom Telesco to get the Chargers back on track in the AFC West. Their primary weapon will be quarterback Phillip Rivers, who endured a long season in large part because of the injury-plagued offensive line.
McCoy helped guide Denver to a solid year on offense. The Broncos ranked second in the NFL in total points with 481, and was fourth in total yards per game and fifth in passing.