The 20-year-old spent just a single season in Italy, which ended in relegation to Serie B, but shone for Colombia at the Under-20 World Cup, as he scored three goals in four appearances.
Quintero, who made his senior national team bow against Chile in 2012, revealed his ambition to win trophies with Porto after being unveiled at Estadio do Dragao.
"I always wanted to come to this club. I come here with great hopes of winning titles," he told the club's official website.
"I am very happy, for this is an important step in my career. Now my main concern is working hard every day."
The midfielder, who played for Envigado and Atletico Nacional during his formative years, has had a £34.5 million release clause inserted in his contract and reportedly caught the eye of Inter and Udinese before joining Porto.
Quintero made 17 Serie A appearances last season, scoring one goal.