The 26-year-old seals a move to the Scottish Premiership following an 18-month spell with the Reds, having joined the club from Preston North End.
Davies was named on the bench eight times in the second half of 2020-21 after his arrival, before then heading out on loan to Sheffield United for the duration of 2021-22.
He returned to Liverpool for the start of the current pre-season and has now finalised a move north to Rangers, with Jürgen Klopp delighted to see the centre-back secure such an opportunity.
“Super move. Very positive outcome,” the manager told Liverpoolfc.