The 18-year-old made his debut last season after progressing through Rovers' youth academy and has scored five goals in as many starts and 18 substitute appearances.
Manager Ronnie Moore said: "Cole is a promising young striker who deserves this opportunity.
"We've seen glimpses of his talent this season and I believe there is a lot more to come from him.
"He has a great attitude, wants to improve and has a bright future at the club."
Stockton added: "I'm really pleased with my new contract.
"I'm grateful to the manager for giving me this chance and hopefully I'll repay him and the club with my performances."