Kounde, 23, was the subject of several bids from Chelsea last summer, and reports suggested he was close to a move to the English side at the end of last week.
However, Barca upped their interest over the weekend, with sources telling ESPN that coach Xavi Hernandez's insistence on signing the centre-back has been key in getting the deal over the line.
Barca president Joan Laporta also said in an interview with ESPN last week that Chelsea, along with Paris Saint-Germain, had also tried to sign Robert Lewandowski, who joined the Blaugrana from Bayern Munich for €45m earlier this month.
The France international joins Barca after three years in Spain with Sevilla, during which time he made 133 appearances, scoring nine goals. He joined Sevilla from Bordeaux for around €25m, and they are due a percentage of the fee from his switch to Camp Nou.
He is Barca's second centre-back signing of the summer after Christensen joined on a free transfer from Chelsea. Xavi also has Ronald Araujo, Gerard Pique and Eric Garcia as options at the back, while Kounde and Araujo can both play right-back, too.
Barca's spending has been fuelled by the sale of 25% of their domestic television rights to the investment firm Sixth Street for the next 25 years for around €530m. The rights are worth around €160m annually to the Catalan club.
However, to get back within their LaLiga spending limit -- which was -€144m at the end of last season, the only negative cap in the league -- and to be able to register all their new signings, as well as the new contracts signed by Sergi Roberto and Ousmane Dembele, Barca still need to move other players on.
Neto, Oscar Mingueza, Samuel Umtiti, Riqui Puig and Martin Braithwaite were all left out of the tour of the United States to allow them to find new clubs, while Barca are also open to offers for other first-team players.