Neymar was paraded as the Spanish champions' marquee signing when they beat off competition from Real Madrid to lure him from Santos in the close season and the club said he had cost 57.1 million euros (£47.1 million).
However, precise details of the contract were not revealed with Barca pointing out the existence of confidentiality agreements. A club member, Jordi Cases, having not received the information he requested about the deal, then took legal action.
Rosell denies wrongdoing and the club reacted angrily after the state prosecutor asked the judge to open proceedings for possible misappropriation of funds.
Neymar's signing was "complex" and an example of "business engineering" and they would act forcefully to defend the honour of the club and the president, Barca said.
"Having anticipated you would ask about this, there are two points I would like to make," Rosell told a news conference on Monday to unveil Barca's plans to remodel their stadium.
"The first is a reaffirmation...that Neymar cost 57.1 million euros, full stop. I am saying it for the umpteenth time and that's enough now.
"The second is a request, with all my respect for the judge in this case. I ask him to initiate proceedings and calls me to testify, precisely so I can tell the judge anything he would like to hear because there is nothing to hide," said Rosell.
"Everything is absolutely legal and absolutely clean. Any confidentially clause that existed was always because it was asked for by the other side."
Spanish daily El Mundo reported on Monday it had access to court documents that showed Neymar had cost a total of 95 million euros including various commissions and fees paid to the player's family.
That would make him the second most expensive player in history after Real paid Tottenham Hotspur 100 million euros for Wales winger Gareth Bale last year.
In an interview with Barcelona-based daily Sport last week, Neymar said he believed there was nothing illegal about his transfer.
"I know that a lot is being said about my contract. I have spoken to (my father) to see what they were talking about exactly. My father was the one who signed the contracts and he is someone in whom I have total trust," the 21-year-old said.
"There is nothing illegal. If anyone has any doubts they should ask my dad because I'm concentrating on my job which is playing football."