Still, it said there were a number of issues that needed further investigation.
"The ad hoc group will make early recommendations for decision by the executive directors," the board said.
Wolfowitz pledged on Friday to abide by the recommendations of the board.
In a brief statement, the embattled World Bank chief said he "welcomes the decision of the board to move forward and resolve this very important issue".
The statement said Wolfowitz "looks forward to implementing the recommendations of the board".
Wolfowitz has faced calls by World Bank staff for his resignation and questions about his leadership over his handling of the promotion for Shaha Riza, a former senior communications officer at the bank.
Over the weekend, World Bank shareholder governments said they were deeply concerned that the scandal had damaged the bank's credibility and could prevent the institution from functioning properly.
Senior Democratic ministers and other critics have demanded Wolfowitz's resignation, saying his actions have undermined his campaign against corruption in the developing world.
"Wolfowitz must resign because... his act of favouritism for personal interest was wrong"
Ibby, Mumbai, India
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Wolfowitz has said he does not intend to step down and last week he apologised for how he handled Riza's promotion, saying he was new at the bank when it was arranged.
The White House has repeated its support for Wolfowitz, who had been nominated by George Bush, the US president, to head the World Bank in 2005.
The US is the World Bank's biggest shareholder, holding 16.4 per cent of total board votes, followed by ally Japan which has 7.9 per cent.
A major decision by the board requires an 85 per cent majority, with the US holding enough votes to block any major decision.