The 53-year-old replaces John Gregory, who parted company with the club last week after a poor start to the season that sees them second bottom of the table.
Coyle will manage the two-time Indian Super League champions until the end of the 2019-2020 season.
Speaking with the club's media team, he said, "I am incredibly proud to join Chennaiyin FC as their head coach.
"It will be my immense privilege to join a club with so much success already in its early history with two ISL titles. I believe we possess a squad with great potential and the hunger to do well, complimented by an ardent fanbase always backing us. I can’t wait to get started."
“Owen (Coyle) is a renowned name in British football, with a fantastic career as both player and coach