The 16-year-old midfielder will join the club’s Under-18, managed by Cameron Campbell and Stevie Smith.
Bell is a Scotland youth international, making an appearance for the country’s Under-17 side in a draw with Wales at Forthbank Stadium.
The teenager announced he was leaving Everton back in May after spending nine years with the Premier League side.
He said: “Some of the best moments of my life playing for this football club and wouldn’t change a single thing. Thanks to every person at Everton that made me into the person and player that I am today.
"Hopefully things will return to the way they once was at the club soon enough. Gonna be strange not putting that kit on anymore but cannot wait for the next chapter.”
He is the latest young star signed by Rangers, following the additions of the likes of Cameroon Cooper from Patrick Thistle and Kieron Willox from Inverness CT.