The EU Commission has taken office amid a new row over one of its members - the French transport commissioner.
Barrot did not disclose his conviction during his confirmation hearings
MEPs urged a review of Jacques Barrot's position when it emerged he had failed to reveal a conviction for embezzlement - later quashed under a French amnesty.
But Commission President Jose Manuel Barroso reaffirmed his confidence in Mr Barrot, saying he would make an "excellent commissioner".
The Commission is already starting work three weeks late due to a previous row.
Mr Barroso had to withdraw his original line-up last month after some lawmakers in the European Parliament objected to Italian nominee Rocco Buttiglione's outspoken views on women and homosexuality.
The vote was finally passed last Thursday.
'Nothing to cover up'
The latest row erupted last week when Britain's anti-EU UK Independence Party (UKIP) revealed Mr Barrot's 2000 conviction in the European Parliament and demanded his resignation.
Mr Barrot received a suspended prison sentence for party funding offences, but it was immediately voided by a 1995 presidential amnesty.
On Monday, Mr Barrot released a letter to the president of the European Parliament clarifying the legal case around his conviction.
In the letter, made public by the Commission, Mr Barrot acknowledges he was "the object of a judicial procedure opened in 1995 and closed on February 23, 2000 concerning all leaders of the Centre of Social Democrats [CDS]", Reuters news agency reports.
Mr Barrot goes on to point out he has never been barred from holding public office.
"I had nothing to cover up and I absolutely did not look to
cover up anything from the European Parliament, which I profoundly respect," he writes in the letter.
A Commission spokeswoman said Mr Barroso believed Mr Barrot had now explained his position satisfactorily and should be allowed to begin work.
"Mr Barroso feels that under these conditions Mr Barrot will be an excellent commissioner," the spokeswoman said.
Earlier, however, Martin Schulz, leader of the parliament's second-largest group, the Socialists, demanded Mr Barrot meet senior parliament officials to discuss his past, AP news agency reports.
He added to demands from Graham Watson - who leads the third-largest group in the European Parliament, the Liberal Democrats - that Mr Barrot resign or be suspended until the matter is fully resolved.
Mr Watson said Mr Barrot had been "seriously compromised" by the revelations.
BBC Europe correspondent Tim Franks says the problem is not so much the crime as the perception of a cover-up.
Mr Barrot did not provide a full account to the parliament of his past activities in his confirmation hearings two months ago.
And a French amnesty law prevented the media reporting the details of the procedure that Mr Barrot faced.
Mr Barroso said in an interview he wanted to get on with the work of the commission - including pushing economic reform in Europe and deciding whether to open membership negotiations with Turkey.
Mr Barroso opted to withdraw his entire team on 29 October rather than have it rejected by parliament, after a bruising row broke out over the choice of Mr Buttiglione as justice commissioner.
Italian Prime Minister Silvio Berlusconi was forced to replace Mr Buttiglione - who angered many MEPs by describing homosexuality as a "sin" - with outgoing Foreign Minister Franco Frattini.
In other changes, Hungary's socialist nominee, Laszlo Kovacs, was reshuffled to the taxation and customs job and Latvia replaced its candidate.
However, Mr Barroso did not give in to MEPs' requests for him to replace the Dutch nominee for the post of competition commissioner, Neelie Kroes.