Martins Indi had reportedly been a transfer target for Louis van Gaal, the outgoing Holland manager who officially takes charge of Barclays Premier League club Manchester United this week.
Speaking through Feyenoord’s official Twitter account, Martins Indi said: "I’ve always said that if I left the club then it would be to make a step up.
"As well as saying a special ‘thank you’ to my team-mates, I would like to thank the Feyenoord fans for their unconditional support."
A further tweet from the Rotterdam club read: "After many years at Feyenoord we would like to wish Bruno every success with Porto and in his future career."
The left-footed Martins Indi graduated from the youth academy at De Kuip to make 102 Eredivisie appearances for Feyenoord and, having made his Holland debut in 2012, has so far earned 22 senior caps with the Oranje.