Bartomeu, Rosell and club are accused of defrauding the tax authorities of around 13 million euros (9.26 million pounds) between 2011 and 2014 by trying to hide the real cost of the deal.
Rosell initially said Neymar had cost 57.1 million euros but the club later admitted a host of additional contracts with the player and his father had pushed the value of the transfer closer to 100 million.
Judge Pablo Ruz decided there was enough evidence to proceed with a trial on charges of tax fraud and maladministration, court documents published on Friday showed.
Barca announced they would appeal the decision and said they believed the evidence did not show a crime had been committed.
In a statement on their website, the club added that their members, who are due to vote for a new president at the end of the season, should remain calm.
Bartomeu, a vice president under Rosell who was involved in negotiating the Neymar transfer and is standing for reelection, said at a court appearance last month that neither he nor the club and its officials had intentionally committed tax fraud.
Barca coach Luis Enrique told a post-training news conference on Friday he and his squad were focussing on playing football.
The La Liga leaders, who play at Eibar on Saturday, have a chance of repeating their historic 2009 treble of Spanish league and Cup and Champions League this season.
They have a one-point advantage over second-placed Real Madrid in La Liga, take a 2-1 lead into Wednesday's Champions League last 16, second leg at home to Manchester City and are through to the King's Cup final.
"What we have control over are the training sessions, everything else is in the hands of the justice system," Luis Enrique said when asked about the tax fraud trial.
"We will see what happens when there is a final decision on the matter," he added.
"Unfortunately we are used to controversy, rumours and this sort of news but we have to carry on with our job."
(Additional reporting by Elena Gyldenkerne in Barcelona, writing by Iain Rogers, editing by Toby Davis)
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