Cotterill played second fiddle to Redknapp as they helped the Blues remain in the Championship during their three-game period at the end of the season, but while Redknapp will remain at St Andrew's, Cotterill has rejected the opportunity to stay in the West Midlands.
The 52-year-old told the club's official website: "It was a very difficult decision. I have given it a lot of thought, but I have decided to turn down the club's offer of being assistant manager.
"The club made me a good offer and my decision was solely based on being a number two, whereas really I have been a manager for a long time in my own right. Harry Redknapp asked me to come in and help for three weeks and I believe that's what I firmly did."
During a 20-year managerial career, Cotterill has been in the dugout on 661 occasions, managing seven teams across four divisions from the Football Conference to the Championship.
His most recent achievement came in the 2014-15 campaign as he helped Bristol City to the League One title.