The deal for the 20-year-old had long been rumoured, and a season-long loan deal has now been agreed - with an option to purchase at the end of the season thought to be part of the agreement.
"I'm very happy to have signed for a club like Liverpool. I think it's one of the biggest in Europe. Any footballer would want to come and play here," he said.
"When they tell you Liverpool want to sign you, I think like any player, you are going to be absolutely amazed and you don't think of anything else than going straight there.
"It's a team that nowadays, as I said before, any player would want to be a part of."
Manquillo, who also interested Arsenal, will provide competition for England international Glen Johnson, who is in the final year of his contract but has reached an impasse with the Reds over a new deal.
The club had wanted the defender to sign a contract on reduced terms considering the basis he turns 30 next month but Johnson does not want to accept that.
VIEW FROM SPAIN
Eurosport's Patrik Hernandez gives us his expert view on Manquillo: "He first made a splash last year, but he played a few games with the first team in the 2012-13 season. He was unlucky to get very badly injured in February after a tough clash with Cristiano Ronaldo (below) - an injury that made front page headlines in Spain.
"He's fine now but really desperate to play, and he knows he won't get in the Atletico team ahead of Juanfran. So Liverpool have got a great player, and his potential is as great as that of any right-back in Spain.
"His best quality is his ability to steal the ball from an opponents and start attacking moves, taking advantage of his stamina and huge stride length. Defensively he's good enough, but he's got room for improvement."
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