The 18-year-old has agreed a deal to keep him with the Championship side until 2015 after a successful trial period.
Forrester joined the Toffees' academy aged nine and went on to feature regularly for the Under-16s and Under-18s.
More recently the youngster had been on the fringes of Alan Stubbs' development squad, making seven appearances for the Under-21s this season.
Rovers have also confirmed the departure - by mutual consent - of midfielder Amine Linganzi.
The 23-year-old joined the club from French side St Etienne in 2010 but has made just four appearances.