The magistrate investigating the case in Madrid agreed with the decision of the public prosecutor to drop charges against Bartomeu and the club's vice-president Javier Faus, who looks after the club's finances.
Barcelona initially said that the signing of Neymar had cost them €57.1 million euros ($72.5m)
However, one of Barcelona's own members, or 'socios', Jordi Cases, accused the club's former president Sandro Rosell of misappropriation for not declaring publicly that 40 million of the figure quoted by Barca was paid to N&N, a company controlled by Neymar's parents.
Judge Pablo Ruz widened his investigation earlier this year when he decided that there was "sufficient evidence to investigate a possible crime against the public treasury".
Barcelona and Rosell, who stepped down in January, were accused of irregularities in the deal, which was worth a total figure of just over €86 million.
But on Friday the judge concluded that there was no reason to pursue charges against Bartomeu and Faus, former right-hand men of Rosell under the previous presidency and who signed certain incriminating documents.
Ruz ruled there was not enough evidence to suggest that the two had "actively participated in the facts under investigation".
Prosecutor Jose Perals said that, in the case of the alleged tax crimes, responsibility falls to the club as a whole and Rosell, as he was president at the time.
The Barcelona board have been rattled for several months by the investigation into the signing of Neymar in the spring of 2013 and the father of the Brazilian star is still due to appear as a witness on October 1 as part of the case.
Bartomeu tried to calm the controversy after taking over as president by disclosing the exact figures of the transfer, which was valued at €86.2 million euros, and paying €13.5 million to the public purse.
Rosell, who gave evidence for several hours on July 22, insisted before the judge that the transfer was carried out legally, affirming that "the contracts were perfectly drawn up".