Chudzinski, 46, spent this season as special assistant to head coach Chuck Pagano. He previously coached the Cleveland Browns in 2013 and was fired after finishing 4-12 in his lone season as head coach.
"We're excited to keep Chud in our family," said Pagano. "He's been a critical part of our operation and we're looking forward to sharing even more success in the future."
Chudzinski has been an offensive coordinator twice before in the NFL, first with the Browns in 2007 and 2008 and then with the Carolina Panthers in 2011 and 2012.
The Colts finished 11-5 and won the AFC South this season. They lost to the New England Patriots in the AFC Championship.
- Paul Palladino