The teenage trio are second year scholars and are key members of Shaun Garnett's under-18 set-up at Prenton Park.
Stockton, 18, made his first-team debut as a second-half substitute during January's goalless draw with Rochdale and is the top scorer for Rovers' reserve and youth teams this season despite also spending time on loan with Blue Square Bet North outfit Vauxhall Motors.
Non-league football has also played a part in the education of 18-year-old centre-back Vaulks, who enjoyed a spell at Evo-Stik League Division One North side Cammell Laird this term, while attacking midfielder Kirby, 17, has featured regularly at reserve level.
"I'm delighted for all three - it's always a special day when you're offered your first professional contract," Garnett told Tranmere's official website. "They've now go to make sure they continue the hard work that got them this far."