The 24-year-old winger, who started all three of Ecuador's group games against France, Switzerland and Honduras during the World Cup in Brazil, has agreed a four-year deal for an undisclosed fee. Montero went straight into training with the Swans on Thursday after passing a medical. He has moved to the Liberty Stadium from Mexican club Morelia.
He becomes Swansea's latest new signing of a busy summer, quickly following Gylfi Sigurdsson, whose move from Spurs was confirmed on Wednesday, while other new arrivals have included ex-Arsenal goalkeeper Lukasz Fabianski and former Lyon striker Bafetimbi Gomis. Montero previously played for Villareal, and he lined up against Swansea while on loan at Real Betis in a friendly three years ago.
The Swans, meanwhile, have confirmed Alejandro Pozuelo's Liberty Stadium departure to join Primera Division side Rayo Vallecano. Swansea said on their official website that midfielder Pozuelo had signed for an undisclosed fee.
The 22-year-old Spaniard moved to Wales from Real Betis last summer, but he has not featured for the Barclays Premier League club in recent months. He signed a three-year deal with the Swans, having been recruited by current manager Garry Monk's predecessor Michael Laudrup.
Pozuelo made 36 appearances and scored two goals, but he last played for Swansea when they took on Europa League opponents Napoli in February. Pozuelo's new club posted a picture of him holding a Rayo Vallecano shirt on their official Twitter account on Thursday.
"I was impressed by Swansea when I played against them in a friendly (at the Liberty) while I was at Betis. Their style is very attractive," said Montero, who spoke via a translator on Swansea's website. "And Antonio Valencia also spoke very well about the team -- he said they are always a tough team to play against. We've spoken recently and we joked about Swansea and Manchester United playing in the first game. So that will be an interesting match for us.
Montero added: "He also told me how great the league is. Every single game is very competitive, and I'm really looking forward to playing in it. I've played in La Liga and in Mexico, but now I am in the Premier League â the best in the world - and I want to thank Swansea for giving me this opportunity."