The striker scored on the final day of last season to help the club win the National League South.
He has been expected to remain and be a part of their third push for promotion in three years.
But the former Crawley, AFC Wimbledon and Portsmouth striker will instead play next season for Southern League Gosport Borough. He will be player-coach at Privett Park.
Havant have been busy in the close season and have signed forwards Nicke Kabamba and Alfie Pavey.
But the duo who helped them to the title, Tubbs and Jason Prior, have both decided to step back.
Tubbs tweeted: “Would like to thank everyone involved @HavantWvilleFC from the Manager, Staff, Players and Fans.
“Wishing the club all the best in the @TheNationalLge Now my focus is on a new challenge @GosportBFC”