Volcker, along with UN Secretary-General Kofi Annan, had called for a resolution to give the investigation political footing among governments, some of whose officials and firms are accused of getting and giving kickbacks to Saddam Hussein's government.
"We will be following the money as well as we can," Volcker told a news conference on Wednesday, held simultaneously with adoption of the resolution that "calls on member states, including their national regulatory authorities, to cooperate fully by all appropriate means with the inquiry."
"I wanted a resolution to make sure that member governments and member states knew what they were getting into," Volcker said of the 15-nation Security Council action.
Volcker, 76, has been a major architect of US financial and economic policy, serving five presidents from John F Kennedy to Ronald Reagan.
Other members of the board are Judge Richard Goldstoneof South Africa, who served as the first prosecutor on the UN Balkan war crimes tribunal, and Swiss lawyer Mark Pieth, an expert on international bribery and money laundering.
Volcker said he would have his first report within three months but predicted the investigation would take much longer.
"I didn't agree to do this lightly," Volcker said. "But there are some very important accusations made about the UN"
"I wanted a resolution to make sure that member governments and member states knew what they were getting into"
former chairman, US Federal Reserve
Allegations of payoffs, favouritism and surcharges on oil were reported by UN officials and others to a divided Security Council for years and sometimes resulted in action.
New, however, are lists of those who allegedly received bribes, including politicians and businesses around the world.
Benon Sevan, the former head of the UN programme, is among those accused of taking a bribe and has vigorously denied it.
Volcker said the most important task was to find out if there was substance to the allegations. "If there is substance, get it out there, get it out in a hurry and cauterize the wound," he said.
The US General Accounting Office, the investigative arm of the US Congress, says Iraqi elites pocketed $4.4 billion by imposing illegal surcharges on oil sales.
Under the plan, Iraq was permitted to sell oil in order to buy civilian goods. The purpose was to ease the impact on ordinary Iraqis of sanctions imposed after the 1991 Gulf War.