Kotwica, 21, joined the Tigers as a free agent in July 2016 after being released by neighbours Cheltenham Town and became a key part of Tim Harris’ National League North side, scoring 13 league goals in forty-four appearances.
During his time at the club, Kotwica made sixty-five appearances, scoring 16 goals in total.
The deal is structured to include future incentives.
Speaking on the transfer to the club`s official website, Gloucester manager Tim Harris said: “Unfortunately it’s an indictment of where we are as a football club that we have to seriously consider offers when we receive them due to a lack of commercial revenue and support from local businesses this season.
“I have been given assurances by the owner of the club that we will be home before the end of next season and until we get home we’re just trying to survive, but it’s getting very difficult to do so.
“I must state we didn’t want to lose Zack a local lad though it’s an opportunity he couldn’t turn down. We wish him well and hopefully he can progress back into the professional game.”
Gloucester chairman Mike Dunstan OBE echoes the sentiments of Harris: “We wish Zack all the best at Tamworth and it’s unfortunate to see him go, but as Tim said, we have to seriously consider offers for players when they come in because of where we are as a club.
“Our commercial income streams have been drastically hit with the move to Evesham, but we have to deal with it.
“Everybody is working incredibly hard behind the scenes to bring in extra revenue to the club as we aim for our return home next season, but we’re only human and we need support of Gloucestershire businesses to keep the club sustainable.”
The 21-year-old was recalled from a loan spell with Evo-Stik League South West side Salisbury FC to complete his move to The Lamb.
He joined up with Steve Claridge's side on October 25th, making his debut in the 5-4 win at Winchester City.
He grabbed his first goal in the next game, a 2-0 win at Barnstaple Town, and the highlight of his spell at the Ray Mac was a hat-trick against Swindon Supermarine in the Wiltshire FA Senior Cup.