The Gers have paid an initial fee of £6.5m, with a further £1m due in performance-related add-ons. Liverpool have also included a 20 per cent sell-on clause to the deal.
Speaking exclusively to RangersTV, Kent said: "I am delighted to be back here, it has been a quite a long summer, a lot of things could have potentially happened but I am delighted to be here.
"I never lost hope, there were probably moments when I thought it might not happen but I guess good things come to those who wait.
"I won't lie it has been incredibly tough over the summer but I am a mentally strong person as it is anyway.
"I knew if I kept myself correct something good would happen soon and I have been ticking over, keeping myself to myself and this has happened now and I'm over the moon."