Schottenheimer, 42, was most recently the offensive coordinator and quarterbacks coach at the University of Georgia.
He was also the offensive coordinator for the St. Louis Rams (2012-14) and the New York Jets (2006-11), and he had stints as the quarterbacks coach for the San Diego Chargers (2001-05) and with Washington (2001).
During his time in San Diego, Schottenheimer worked with current Indianapolis offensive coordinator Rob Chudzinski, as Albert Breer of NFL Network noted.
The pair will be tasked with building an offense around franchise quarterback Andrew Luck and ensuring that he continues to progress.
That progression took a detour in 2015 after injuries cost Luck over half of the season, though he still threw for 1,881 yards and 15 touchdowns in seven games. His 12 interceptions during that time were a concern, however, as he was on pace to easily eclipse his previous high in interceptions, 18, thrown during his rookie year.
The Colts will only go as far as Luck can take them, so reducing his turnovers will be a priority for Schottenheimer in Indianapolis. Luck seemed poised to enter the elite pantheon of quarterbacks in 2014 after throwing for 4,761 yards and 40 touchdowns, so getting him back on that path will be Schottenheimer's most urgent priority.