The 17-year-old is son of former Hearts and Falkirk goalkeeper Myles Hogarth and younger brother of Rangers goalkeeper Nicky – currently on loan at Cowdenbeath.
Hogarth has been with Rangers from a young age and signed his first professional deal with the club in 2019, and the new deal will extend his stay with the club for another three seasons.
The teenager, capped for Scotland under-17s, was one of the youth prospects named among Rangers’ Europa League B list – the homegrown section of the squad eligible to be called upon for this season’s competition, which included Leon King and Nathan Patterson who were both selected in matchday squads by Steven Gerrard.
Dad Myles is currently goalkeeper coach with East of Scotland Premier Division side Linlithgow Rose and played more than 100 games with Falkirk after leaving Tynecastle. He also turned out for Stirling, Alloa and Hamilton.