Semedo arrives at Molineux in a reported €35m ($41m) transfer as a replacement for Matt Doherty, who joined Tottenham last month.
The Portugal international, who spent three years at Camp Nou after signing from Benfica, posted a message to Barca on his Instagram page on Tuesday before Wolves confirmed his arrival the following day.
Semedo wrote: "Thank you very much Barcelona for giving me the dream of wearing this shirt. Thank you for making me grow as a player and as a person.
"I've had three wonderful years that I won't forget. I want to thank my team-mates, the staff, the fans and all the people who have helped me from the moment I arrived until today."
Semedo is the latest player to leave the Blaugrana as new coach Ronald Koeman overhauls the first-team squad following a dismal 2019-20 campaign.
Welcome to Wolves, @_nelsonsemedo_!— Wolves (@Wolves) September 23, 2020
The 26-year-old featured 42 times in all competitions last season, scoring once, as Barca lost their LaLiga crown, failed to win a trophy and crashed out of the Champions League in humiliating fashion, going down 8-2 to Bayern Munich.
Arturo Vidal has left for Inter, while Luis Suarez is also expected to depart. The club blocked captain Lionel Messi's exit.
Semedo's departure had been anticipated, with Barca linked with bids for alternative right-back options - including Arsenal's Hector Bellerin, Norwich City's Max Aarons and Ajax's Sergino Dest.
Contrasting reports have Aarons and Dest close to moves to Catalonia.
Semedo was welcomed at Wolves, where his new contract has the option for a further two years.
"It isn't often that we have the opportunity to sign a world-class player from a world-class club," executive chairman Jeff Shi said. "Nelson's signing shows we will never stop progressing and we are still hungry and humble in our heart."
Semedo, a two-time LaLiga winner, added: "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."