The 26-year-old centre-back has arrived at Ibrox in a reported £4million deal ahead of the imminent departure of Calvin Bassey to Ajax.
Davies almost signed a pre-contract deal with Celtic 18 months ago before Liverpool swept in to sign him in an immediate transfer from Preston as they battled an injury crisis in central defence.
The defender, who spent eight years with North End, never played for the Reds and last season went on loan to Sheffield United, where he made 23 appearances.
Davies said on his new club’s website: “I am very excited to join Rangers and I am really looking forward to taking this next step in my career.
“It’s a huge club with big ambitions and I can’t wait to get started.”
Liverpool boss Jurgen Klopp praised his Rangers counterpart Giovanni van Bronckhorst for “smart recruitment” as he paid tribute to his departing defender, despite failing to select him for any competitive matches during his time at Anfield.
“Rangers is a fantastic club, a big club. Ben belongs on a big stage for sure,” Klopp told the Liverpool website.
"This presents a proper opportunity to demonstrate his quality and composure.
"As a person he’s a good guy as you could hope to meet.
"It’s a smart piece of recruitment from Giovanni van Bronckhorst. Perfect for all parties.
"He has himself an accomplished defender, who is entering his peak years and whose character is top drawer.”
Van Bronckhorst said: “I would like to welcome Ben to our squad and I am delighted he has joined the club. He is a strong defender with great qualities and will further add to our options in that area."
Rangers Sporting Director, Ross Wilson, added: “I am delighted Ben has chosen Rangers as the next step in his career and Giovanni and our coaching staff are looking forward to working with him as we head into the new season.”