The Colombia midfielder joins the Portuguese side for £4.3m (€5M) after starring in the Under-20 World Cup in Turkey, scoring three goals in four appearances.
The 20-year-old, who spent just one season in Italy, has revealed that he is hoping to win trophies at Porto and describes the move as "an important step" in his career.
"I always wanted to come to this club. I come here with great hopes of winning titles," Quintero 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."
Quintero made 17 appearances in Serie A last season, scoring one goal in the process.