Moore is the youngest player to have played for Tottenham in the Premier League, having made his debut at the age of 16 years and 277 days in May 2024.
The England Under-19 international also became the youngest player to start a Premier League match for the club in October.
He broke Spurs great Jimmy Greaves’ record of becoming the youngest English scorer in a major European competition during the club’s Europa League-winning campaign last season.
“His profile as a brave, aggressive attacking player is one that we were keen to add to the squad, and he is certainly a player who, despite his age, can make an impact on the team from day one,” said Rangers head coach Russell Martin.
“He is a player with huge potential, and it is testament to his quality that he has been entrusted by Spurs in both the Premier League and Europa League with such regularity over the last 18 months.”