The 23-year-old has signed a three-year contract with the Premier League club after passing a medical.
Manquillo, who has travelled to link up with Rafael Benitez's squad for their pre-season training camp in the Republic of Ireland, will reportedly cost £4.5million.
"I'm very happy to be here. From the first moment that Rafa Benitez called me, I just knew that I had to come here, to such a big club," he told Newcastle's official website.
"I'm very happy with the challenge ahead. I've come here to work hard and give everything on and off the pitch. Hopefully then everything will go in the right direction."
Benitez added: "Like Jacob Murphy, Manquillo is another young player. He can play both sides of the defence and he has a lot of motivation because he knows he has a point to prove.
"He can still improve but he has played for Spain at Under-21 level and that is because he is a good player, so hopefully he will show that form here."
Manquillo spent last season on loan at Sunderland, making 20 appearances in the Premier League under David Moyes.
Newcastle appeared to take a swipe at their fierce rivals when they announced the deal on Friday, tweeting "Some things are just better in black and white", along with a picture of the full-back.
Manquillo follows Murphy, Florian Lejeune and Christian Atsu in joining the club in the transfer window.