The 20-year-old has joined on a two-year loan deal with an option to buy after his first season at Anfield.
Manquillo said: “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.
"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.
"The immediate objective is to do the best I possibly can here. I've come here to try and secure a place for myself in the side and, if possible, stay here for many more years in the future."
Manquillo is a Spain Under-20 international defender who began his youth career at Real Madrid before switching to Atletico in 2007.
After making a 2011 first-team debut, he played 42 times for the club’s B team during the 2012-13 season and has gone on to play five more times for the reigning La Liga champions.
He becomes Liverpool’s seventh signing of the summer following the arrivals of Rickie Lambert, Emre Can, Adam Lallana, Lazar Markovic, Dejan Lovren and Divock Origi.