Oettinger has been at the centre of controversy recently over allegations that he accepted a trip on the private jet of an unregistered lobbyist and held secret meetings with the car industry.
He was also alleged to have made homophobic and racist remarks.
Even so, a majority of the committees' coordinators were satisfied that Oettinger is in a position to assume the budgets portfolio that has been transferred.
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Members said they "look forward to a close working relationship."
A hearing with Oettinger took place on Monday at a meeting of the committees on budgets, budgetary control and legal affairs, following Commission President Jean-Claude Juncker's decision to transfer the budget and human resources portfolio to Oettinger after Vice-President Kristalina Georgieva resigned.
The digital economy and society portfolio, which Oettinger held until the end of last year, was temporarily assigned to Vice-President Andrus Ansip by Juncker.
Corporate Europe Observatory's lobby transparency campaigner Vicky Cann said, "Oettinger has long been a buddy to business and has a track record of protecting car industry interests from environmental regulation.
"Even in 2016, as Commissioner for digital economy, he had six meetings with the car industry, including two with scandal-struck Volkswagen group."
She added, "We continue to demand an independent Commission ethics body which can launch its own investigations into allegations against both former and current Commissioners."