The 18-year-old, who made his first-team debut against Carlisle earlier this season, has agreed a one-year deal at Prenton Park.
He has scored 27 goals for Rovers' reserve and youth teams this season and manager Ronnie Moore is hoping for a bright future for the youngster.
"Josh is a promising young player and a proven scorer at youth level," said Moore. "He has a knack of finding the net and hopefully that will continue in his professional career.
"It shows the hard work being carried out at the Centre of Excellence through to the Youth Team is paying off. It is fantastic to see another player come through who has been with us since a young age."