The Portuguese full-back signs for Wolves as a direct replacement for the departed Matt Doherty, who left the club for Spurs earlier this summer.
The club had already bolstered the position with the signing of Ki-Jana Hoever from Liverpool - but Semedo offers a more experienced option on the right flank, having made more than 100 appearances for Barcelona.
Semedo has signed a deal that will keep him at Molineux until 2023, with an option to extend until 2025 in the club's favour.
Wolves will pay an initial £27.5m for the 26-year-old, although add-ons could see that rise to £29m and potentially even more should certain triggers be hit.
Jeff Shi hailed the signing, labelling Semedo as a 'world class' acquisition for the club.
"'Progressive at heart' is one of our core values at Wolves. For a member of staff, for a player, for the whole club, we are all making great efforts to progress continuously.
"It’s isn’t often that we have the opportunity to sign a world-class player from a world-class club. Nelson’s signing shows we will never stop progressing and we are still hungry and humble in our heart."
Semedo could feature in Wolves' next game, as they're due to travel to West Ham this weekend.
The defender is excited to start his Wolves career and is hopeful the side can break into the top six during his time at Molineux.
"I chose Wolves because it’s a very good team that plays very good football. Last year they did a very good season and it’s a very important team in England, in also Europe. I hope this year we can do very good things." he said.
"Coach Nuno is a very good coach. He did very good things here in Wolves, and in other teams too. For sure I’m going to learn a lot from him.
"The team did very good things the last three years. I’m ambitious and I hope this year we can do very good things, reach the top six and, if it’s possible, do something special.
"I’m very happy to be here. I’m excited to get started and thank you very much for your support and we’re going to enjoy it together.
"I can bring the team pace, speed. I like to go forward and come back. They can expect a lot of work and a lot of ambition.
"I’m very excited to be here. It’s a very good team. To play in the Premier League is a dream from me too. So, I’m very excited to begin, to meet my teammates and start training.”