The Gloucester-born 18-year-old scored spectacular first goal for the club in last Saturday's 1-1 draw at Mansfield Town and boss Paul Buckle said he was delighted to tie the exciting prospect down for another 18 months.
"It's fantastic to have a local player involved and he is a real talent," Buckle said.
"These young lads need to be given their chance and Zack has shown me enough in the three weeks I have been here to earn a new contract.
"He is willing to learn and I have high hopes for him."
Buckle has been keen to stress the need for Kotwica to work on the defensive side of his game, but he said the academy product's attacking talent will also be carefully nurtured.
"Zack is at his best when he is allowed to go and express himself," he said.
"He has natural ability and he can beat players and score, which he showed at Mansfield and that was an unbelievable goal.
"He still needs to learn the game and myself and Rob Edwards (assistant manager) will be enforcing that, which is what he needs to do to become a regular starter.
"There is a lot of positivity around the place at the moment and when you have young talent, you need to nurture it and by offering Zack another year on his deal it shows what we think of him.
"The challenge for him now is to develop into a regular in the team because we need to be producing our own players."
Kotwica becomes the second player to sign a new deal this week, following Omari Sterling-James, who has also extended his deal until the summer of 2016.