The 18-year-old has joined from Aberdeen for an initial £4m which could rise to £6.5m with bonuses.
Ramsay joins Fabio Carvalho and Darwin Nunez in moving to Anfield this summer.
The Scotland u-21 international has signed a five-year contract with Jurgen Klopp's side and will provide competition for Trent-Alexander Arnold in the right back position.
"I'm just buzzing and it's a dream come true really to be here," the defender told Liverpool's official website after completing his move.
"It was a dream come true to play for Aberdeen, and now to be at one of the biggest, if not the biggest club in the world, it's a massive achievement and I'm looking forward to trying to show the fans what I've got.
"Hopefully I can come in in pre-season, show everyone at the club, the staff, players what I've got and then we'll see what happens from there."
Liverpool manager Jurgen Klopp added: "He is only 18 years old at the moment, although he turns 19 soon, and already has a decent number of first-team appearances for a defender his age."
"He is athletic, smart, confident, with good technical ability and, always crucial, is eager to learn. So there's lots to like.
"Experiences of European and under-21 international football have been really important for him and his development."
"He and we will have patience with each other. I think we have proved ours is the ideal environment to nurture and harness the qualities and talent of a young player."
Ramsay made 33 appearances for Aberdeen last season, scoring one goal and providing nine assists.
