The Brazil international's close-season move from Santos, which the Spanish club initially said was worth 57.1 million euros (£47.3 million), is being investigated by a court for possible misappropriation of funds following a complaint from a Barca member.
Sandro Rosell, who was named in the lawsuit but denies wrongdoing, stepped down as president on Thursday. He said he wanted to protect the club's image and alleged he and his family had been threatened.
Barca had been reluctant to reveal all the details of the deal, citing the confidentiality agreement, but after a board meeting on Friday, Rosell's successor Josep Bartomeu told a news conference Neymar's father had given them permission to go public.
Barca director Raul Sanllehi reiterated the transfer on its own had cost 57.1 million euros (£47.3 million) including 17.1 million euros (£14.1 million) to Santos and 40 million euros (£33.1 million) as a "compensation fee" paid to a company owned by Neymar's parents.
However, he also detailed other payments around the transfer such as a signing bonus of 10 million euros (£8.3 million) and various other fees paid to the family that took the total cost to 86.2 million (£71.4 million).
Barca are paying Neymar 8.8 million euros (£7.3 million) in wages per season for his five-year contract, said Sanllehi.
"Neymar's father waived the confidentiality agreement because he considers what has happened (to Rosell) to be unjust," Bartomeu said.
The player had received more lucrative offers from some of Barca's rivals but decided to move to the Catalan capital because he believed in the club's project and wanted to play alongside Argentina forward Lionel Messi, he added.
Bartomeu said he and the rest of the board, which has remained virtually unchanged after Rosell's exit, intended to see out their mandate until 2016 even if he or vice president Javier Faus are implicated in the lawsuit.
They also intend to stand for re-election for a further term.
The plan to remodel the club's Nou Camp stadium, with construction due to start in 2017, was one of their main priorities, added Bartomeu.