The 22-year-old will return to Ibrox, this time on a permanent basis having enjoyed a productive loan spell under Steven Gerrard last season.
Kent made 43 appearances and won the Scottish Young Player of the Year award, and has been desperate to make a return to Glasgow this summer.
Liverpool will receive an initial fee of £6.5m, with a further £1m due in performance-related add-ons. Included in the deal is a 20 per cent sell-on clause, which Liverpool insisted upon.
It had looked as though Kent would be forced to stay on Merseyside until at least January, with the Reds unwilling to sanction a loan move for the wideman, which would have been the sixth of his career.
Leeds were keen to sign him permanently and had a £4.5m bid before the Championship transfer window closed last month, while Russian outfit Krasnodar saw a £5m offer knocked back later in August. Belgian side Club Brugge were also keen, while there was interest from at least two French clubs.
Rangers, though, have got their man, Gerrard reacting to Sunday’s Old Firm defeat to Celtic by bringing back one of the stars of last season. Kent travelled to Glasgow for a medical on Monday, and his transfer has been finalised with just minutes remaining in the Scottish transfer window.
He will now be in line to make his second Gers debut when they entertain Livingston on September 14.
The Oldham-born winger joined Liverpool as a seven-year-old, and made one competitive senior appearance for the club, in an FA Cup tie at Exeter in 2016. He enjoyed loan spells at Coventry, Barnsley, Freiburg and Bristol City, with mixed success, before shining at Rangers last term.
He becomes the second player to depart Anfield on deadline day, with teenage striker Bobby Duncan having completed a €2m switch to Italian side Fiorentina earlier on Monday. Duncan, 18, has signed a three-year contract with the Serie A side having made it clear he saw no future for himself on Merseyside.