The head of the EU border agency Frontex has resigned after being investigated by the union’s anti-fraud agency, amid numerous reports of its complicity in illegal pushbacks of asylum seekers.

Fabrice Leggeri, who has been criticised by the European parliament for failure to protect the human rights of people seeking asylum in the EU, announced his resignation shortly before Frontex’s management board were to decide whether to take disciplinary action against him.

In a statement on Friday, Frontex confirmed Leggeri and two other staff members had been investigated by the EU’s anti-fraud agency, Olaf, without elaborating on alleged wrongdoing. Leggeri had been given the chance to comment on the Olaf report at a special meeting of the board on Thursday, where he announced his resignation, Frontex said. “The management board took note of his intentions and concluded that the employment has therefore come to an end,” the statement said.

In a copy of his resignation letter seen by the Guardian, Leggeri said: “I give my mandate back to the management board as it seems that the Frontex mandate on which I have been elected and renewed in June 2019 has silently but effectively been changed.”

The letter was dated the same day as an international consortium of journalists, including the Guardian, revealed that Frontex’s database showed it was involved in illegal pushbacks, forcing asylum seekers trying to enter Greece back to Turkey.

But it was the investigation by Olaf that triggered his resignation. The anti-fraud agency called for disciplinary action against Leggeri and two other Frontex officials, two EU sources told the Guardian. One of the sources said Leggeri was accused of covering up human rights violations.

Separately, German Social Democrat MEP Birgit Sippel, who follows Frontex, was not able to confirm whether Leggeri was facing disciplinary action, but said there had been incorrect use of project funds at Frontex.

A spokesperson for Olaf confirmed an investigation into Frontex was closed on 15 February, but declined to make any further comment, citing confidentiality rules to protect the people involved and “possible follow-up in administrative and judicial proceedings”.

Leggeri, a French national who held senior posts in his country’s interior and defence ministries, has led Frontex since 2015, a period when it was transformed from an obscure EU agency into a central plank of the EU border control policy. After the 2015 migration crisis, EU leaders agreed to give the Warsaw-based agency more powers, staff and money. By 2027, Frontex is due to have 10,000 border and coast guards and its budget has already increased more than 19-fold since its creation in 2006.

As Frontex’s executive director, Leggeri has faced heavy criticism, including from a special committee at the European parliament that last year accused the agency of failing to protect the human rights of asylum seekers.

The cross-party committee said Frontex had carried out only a superficial investigation into alleged illegal pushbacks at the EU’s borders. Leggeri was personally criticised for his failure to appoint 40 human rights monitors as required under EU law, while lavishly staffing his own private office. MEPs found he had appointed 63 people to his private office, more than twice the number of people working in the cabinet of president of the European Commission, Ursula von der Leyen.

A spokesperson for the European Commission said Frontex has a “critically important task, which is to help member states to protect the common EU external borders and to uphold at the same time the fundamental rights in doing so”, the commission spokesperson added. “And to achieve this, Frontex must have in place a stable and well functioning agency.”

The German MEP Birgit Sippel, who speaks for the Socialist group on home affairs, said Leggeri’s resignation was long overdue.

She said: “For years, Leggeri has mismanaged the EU’s border and coastguard agency, significantly harming its reputation and misleading the parliament along the way. The evidence of the need for fresh leadership has mounted since then, and we will scrutinise the succession closely.”

The MEP told the Guardian that she believed he resigned because of the Olaf report. “It seems that the behaviour of people working in Frontex was unacceptable,” she said. The use of funding for projects was not always correct. So there were internal things that were not running well, and it seems that this in the end made Leggeri resign.”

Tineke Strik, a Dutch Green MEP, who led the European parliament’s 2021 inquiry into Frontex, said Leggeri had lost all credibility. “We were waiting for a long time for this [resignation] to happen, but he was pretty well protected by member states,” she said. The volume of allegations against him and his responses – that “were simply not good enough” – had made his position untenable, she added: “Because all of these allegations, and the Olaf report …I think it was unavoidable for him to step down because he lost his credibility.”

The MEP rejected Leggeri’s claim that his job description had been “silently” changed, saying his letter revealed “that he never saw human rights protection as an important part of the mandate”.