The Premier League club said the 26-year-old had signed a three-year deal at Molineux, with an option to extend until 2025.
The Portugal international, who made 124 appearances for Barcelona, joins Nuno Espirito Santo's side after three seasons at the Nou Camp.
Barcelona said Wolves would pay €30 million plus €10 million more in "variables".
"FC Barcelona would like to publicly express their gratitude to Nelson Semedo for his commitment and dedication and wishes him all the best for the future," the club said in a statement.
Semedo told the Wolves website he had chosen the club because they were a quality team that played good football.
"Last year they had a very good season and it's a very important team in England, in also Europe," he said. "I hope this year we can do very good things."
Semedo is looking forward to linking up with his compatriot Nuno and a number of international team-mates at the club.
He said: "Coach Nuno is a very good coach. He did very good things here at Wolves, and at other teams too. For sure, I'm going to learn a lot from him."
Wolves executive chairman Jeff Shi said the signing was a coup for the club, who finished seventh in the Premier League last season and reached the quarter-finals of the Europa League.
"It's isn't often that we have the opportunity to sign a world-class player from a world-class club," he said.
"Nelson's signing shows we will never stop progressing and we are still hungry and humble in our heart."
Earlier this month Wolves signed teenage Portuguese forward Fabio Silva from Porto for a club record fee of 40 million euros and have also added young Liverpool defender Ki-Jana Hoever to their squad.