emedo has signed a contract that will keep him at Molineux until the summer of 2023, with an option to extend it to June 2025.
Semedo becomes a direct replacement for right-back Matt Doherty, who left Wolves for Premier League rivals Tottenham Hotspur earlier this month.
Barcelona took to their official club website to confirm the Portuguese’s departure and wished him luck in his future adventure.
"FC Barcelona and Wolverhampton Wanderers Football Club have reached an agreement for the transfer of the player Nelson Semedo," the La Liga giants' statement reads.
"The English club will pay €30m plus €10m 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."
Wolves chairman Jeff Shi was happy after the Premier League side secured the services of Semedo.
"'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," he said.
"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 won two league titles during his three-year stay in Catalonia.