The agreement, which increases the voting shares of some emerging and developing countries by 3.13 percent, put China behind the United States and Japan, but above Germany, Britain and France.
The outcome, which gives emerging and developing countries a 47 percent stake in the bank, still left some disgruntled.
In addition, World Bank members agreed to a general capital increase of $3.5 billion - the first in more than 20 years - to make up for the heavy lending by the bank during the financial crisis.
The voting changes will also provide an additional $1.6 billion to the resources of the poverty-fighting institution to reflect the growing economic might of emerging economic nations like China.
"China's share has increased because of its growth in the world economy," World Bank President Robert Zoellick told a news conference at the end of weekend meetings of the World Bank and International Monetary Fund.
"We're shifting to a multi-polar economy, the institutions have to shift with them," he added.
But tensions bubbled to the surface after months of tough negotiations, in which some countries were reluctant to give up voting shares and others fought to hang on to theirs.
Zoellick said a new formula for calculating voting power, which would achieve a 3 percent shift, was "far from a perfect process but it was one that allowed us to bring 186 shareholders together because there are always sensitivities." "While all countries agreed they wanted to make this shift, those who had to give up shares obviously would have preferred not to have done so," Zoellick added.
He said members had agreed that for the next review in 2015 they would develop a new methodology to seek a more balanced system.
South African Finance Minister Pravin Gordhan expressed disappointment that some developing countries, which were meant to benefit from the shift, instead saw their votes cut.
"We are disappointed that the process has resulted in dilution of the voting power of some Sub-Saharan African countries, in spite of the collective acknowledgment of the need to protect them," Gordhan said. "We strongly believe that more should have been done to prevent such dilutions." "We consider the progress made to date as a starting point for more robust outcomes in future and urge that conditions should be put in place to ensure the accomplishment of a more meaningful and equitable shareholding by the 2015 review," Gordhan said.
Brazilian Finance Minster Guido Mantega said developing countries are still significantly under-represented based on their weight and role in the world economy.
"Given the rapid changes in the economic landscape, a dynamic formula for shareholding should deliver at least parity in 2015, moving toward equitable voting power," he said.
