An independent commission is to investigate how Wales receives public money from the UK Treasury and look at possible tax-varying powers.
Wales has been funded under the formula since the late '70s
The issue has been central to talks on a possible coalition deal between Labour and Plaid Cymru.
Wales is funded under the Barnett formula, which critics have long claimed does not take into account the nation's needs properly.
But the UK Treasury reacted by saying it had no plans to abandon the formula.
A spokesperson for the Treasury - which has the final say on how public money is allocated across the UK - said the formula was "a fair allocation which reflects population shares in the different nations of the United Kingdom."
As AMs voted unanimously in favour of establishing the commission, Budget Minister Jane Hutt said now was the right time to hold such a review.
It has also been a key issue in negotiations between Plaid, the Tories and Liberal Democrats to set up a so-called "rainbow coalition" .
Labour is five seats short of a majority and ruling as a minority assembly government. Discussions have been under way since the 3 May election on various options which could see Labour either remain in power or be removed.
The funding review announcement came during a debate on a Lib Dem motion calling for an independent commission to investigate issues relating to the funding and financial powers of the assembly government.
Ms Hutt responded to the call by saying: "We've concluded that the time has now come to put in place such an independent commission and I think the commission which we intend to appoint will not only review assembly funding and finance.
"But it will go further than that. It will also consider tax-varying powers including corporation tax... and importantly, borrowing powers.
"It's well-known that for the past two terms we didn't advocate such a commission. The time has now come for this to take place."
Ms Hutt also said that they could not establish a commission "with a pre-determined agenda which is why the independent review is so important".
Plaid leader Ieuan Wyn Jones said: "Plaid has campaigned over a number of years for a needs-based formula to fund Welsh public services."
"We are pleased that the assembly government has finally agreed to create a commission to investigate its funding," he said. "We look forward to start the work on this important issue."
During the debate the Lib Dem AM Jenny Randerson admitted that it would not be an easy process.
But she reminded the chamber that the former Labour cabinet minister Lord (Joel) Barnett himself believed that the formula needed to be reviewed.
The formula was devised in 1978 as a means of deciding how public money was spent across the UK.
Conservative AM Alun Cairns said, however, that there was no evidence that Wales would be better off if the formula was reviewed.
He said that the assembly should have the evidence before calling for a change of policy.
Meanwhile the Royal College of Nursing has joined a cross-section of groups in the fields of transport, health and education to call once again for an independent inquiry into how Wales is funded.
Earlier this week Prime Minister Tony Blair said that the Barnett formula was a "small price to pay" for keeping the UK together.