Turner has been out of work since being fired from his role as head coach of the San Diego Chargers at the end of the 2012 regular season.
New Browns head coach Rob Chudzinski said in a statement: "Norv has been one of the most respected offensive coaches in the NFL over the last 25 to 30 years, and he has had a tremendous amount of success at each one of his stops, as a position coach, coordinator and head coach.
"I was able to learn a great deal in the time that I worked for him in San Diego, and I expect that having him as our offensive coordinator will make a big impact on that side of the ball."
Chudzinski previously worked as the tight ends coach for the Chargers during Turner's tenure with the side.
The Browns have made coaching changes after finishing bottom of their division this season.