The 20-year-old arrives at the Estadio do Dragao for a 5million euros fee while his new contract contains a 40million euros release clause.
Quintero told fcporto.pt: "I always wanted to come to this club. I come here with great hopes of winning titles.
"I am very happy, for this is an important step in my career. Now my main concern is working hard every day."
The attacking midfielder scored three goals in four appearances for Colombia in the recently concluded Under-20 World Cup in Turkey and he made his senior debut against Cameroon in 2012.
Quintero had also attracted the interest of Serie A giants Inter Milan and Udinese during his only season at Pescara, which ended with relegation to Serie B in May.