The document said that the G20 still had to do more in order to prevent a global economic crisis of the current scale from occurring again.
The G20 countries, which account for 90 per cent of the world's economic output, said that they would maintain emergency economic supports until a recovery is assured.
The larger body of countries will supplant the G7 and G8 organisations as the "premier forum for international economic co-operation," the draft document said.
The move to take decision-making on the global economy away from the exclusive club of rich Western nations is a reflection of the power that fast-growing economies such as China and India now hold, analysts say.
"You can't talk about the global economy without having the major dynamic emerging economies at the table," John Lipsky, the deputy managing director of the International Monetary Fund (IMF), said.
In the draft communique, G20 leaders said that they had agreed that emerging economies should have greater voting rights in the IMF.
But Max Lawson, a senior policy adviser at Oxfam, said that the changes that had been suggested were not enough to overcome deep-seated imbalances in the IMF.
"Unless it changes its rules to give poor countries a real say in the way it is run, the IMF will remain the world's rich country club," he said.
The apparent recognition by Western nations that the G20 should be lead decision-making on the global economy comes in the wake of the most severe global economic downturn since the 1920s and 1930s.
The global recession is considered by many analysts to have been sparked by reckless risk-taking in Western financial markets.
The draft said that rules on how much capital that banks must have to absorb future losses should be ready by the end of 2010.
The document also said that pay schemes for those who work in banks and large financial institutions should be overhauled, following criticism that pay bonuses had encouraged an aggressive and reckless culture in the financial markets.
The draft said that pay should be linked to "long-term value creation, not excessive risk-taking", although it did not mention imposing caps on pay, as some European leaders had proposed.
Leaders also agreed to phase out subsidies for fossil fuels to help combat global warming, although no date was set for the process to begin.