The 15-year-old will move for a fee of around £600,000 in the summer after he was convinced to leave the Scottish Premiership side following a visit to Chelsea's Cobham Training Centre.
The Blues beat off competition from the likes of Arsenal, Manchester City, Manchester United, Bayern Munich and Barcelona, who all scouted the youngster. Rangers, meanwhile, were doing all they could to retain their top young talent.
great experience training with the first team pic.twitter.com/MPyNw06M3M— Billy Gilmour (@billygilmourrr) January 25, 2017
He is currently too young to move but he will be able to from his next birthday, which falls on June 11.
Gilmour put in a string of incredible performances for his club in the Under 20s side and for his country with in the Victory Shield, but had long before then been of interest to Europe's elite clubs.
The Ayrshire schoolboy was expected to become Rangers' youngest ever player after training with the first team, but his pathway into the first team will likely be affected by the agreement with the Premier League leaders.