The 27-year-old joined Santa Clara in 2018 following a 12-month stint at Ibrox and played 97 times for the Azorean outfit, scoring 11 goals.
Cardoso helped Santa Clara to a sixth-placed finish last season and qualification for the Europa Conference League qualifying rounds, and was linked with a move to Sérgio Conceição’s side last month.
Speaking to Porto’s website after signing on until 2026, the defender said: “I have no words to describe this moment. It's one of the happiest days of my life, without a shadow of a doubt.
"I still don't believe it. It's a dream come true to reach such a level, at one of the biggest clubs in the world. I am very happy and ready to start working.
"I worked for many years to have this opportunity and I'm prepared to grab it. It's the biggest step in my career and I'm looking forward to getting to work and showing what I'm worth.”
Cardoso also revealed that former Ibrox colleague Bruno Alves, who spent more than ten years at Porto, had convinced him to make the move.
“He was one of the first people I spoke to as soon as the possibility of coming to Porto arose,” he said. “I learned a lot from him, on and off the field.
"He told me he was very fond of FC Porto and wished me all the best.”
The former Gers centre-back will also wear the same squad number during his time at the Estádio do Dragão.
"I asked [Bruno] if he minded me having the number two and he said no, he was very happy that I was the one wearing it,” Cardoso added.
Cardoso arrived at Rangers during Pedro Caixinha’s tenure on a three-year deal in the summer of 2017 but left in July the following year.
The Águeda-born player could be joined by another former Ibrox team-mate in Alfredo Morelos. The Colombian striker’s representative is due to meet with Porto president Jorge Nuno Pinto da Costa this week as the Dragões look to bolster their attacking options.