Having broken into the first team four seasons ago Martins Indi, who was born in Portugal, went on to make 102 league appearances, and was a regular for Ronald Koeman last season as Feyenoord finished second in the Eredivisie.
He started five matches at the FIFA World Cup as the Netherlands reached the semi-finals of the competition before a penalty-shootout defeat to Argentina.
With the World Cup over he is now set to become the latest to leave De Kuip after Koeman and Graziano Pelle moved to Southampton, while Daryl Janmaat is on the verge of joining Newcastle.
Techincal director Martin van Geel revealed the Dutch club had not stood in the defender's way to and wished him well.
"This move comes at a good time for Bruno in his career," he told the club's official website. "A big part of his development has come through Feyenoord and he has become a major player in our first team and has become a full international.
"Now he is ready to move abroad. He is one example of what we do with our talents. We wish Bruno good luck with this new challenge in his career. "
The player himself admitted he felt the need to leave in order to test himself at a higher level, and he hopes Feyenoord can benefit from his departure.
"To me, this feels like the right time to leave," the defender said. "I now have over 100 games for the club and played in a World Cup.
"I have said from the beginning that I hoped that if I ever make the next step in my career that it would be better for myself or the club.
"Feyenoord will benefit financially from my departure while I'm set for a new challenge in Portugal."
Porto have inserted a €40m release clause into the 22-year-old's contract that will run until 2018.