The bank aimed at funding infrastructure projects in developing nations will be based in Shanghai and India will preside over its operations for the first five years, followed by Brazil and then Russia, leaders of the five-nation group announced at a summit.
They also set up a $100 billion currency reserves pool to help countries forestall short-term liquidity pressures.
The long-awaited bank is the first major achievement of the BRICS countries since they got together in 2009 to press for a bigger say in the global financial order created by Western powers after World War II.
The BRICS were prompted to seek coordinated action following an exodus of capital from emerging markets last year, triggered by the scaling back of U.S. monetary stimulus.
The new bank reflects the growing influence of the BRICS, which account for almost half the world's population and about one fifth of global economic output.
The bank will start with a subscribed capital of $50 billion divided equally between its five founders, with an initial total of $10 billion in cash put in over seven years and $40 billion in guarantees.
The bank will start lending in 2016 and be open to membership by other countries, but the capital share of the BRICS cannot drop below 55 percent.
The contingency currency pool will be held in the reserves of each BRICS country and can be shifted to another member to cushion balance of payments difficulties. This initiative gathered momentum after the reverse in the flows of cheap dollars that fueled a boom in emerging markets for a decade.
"It will help contain the volatility faced by diverse economies as a result of the tapering of the United States' policy of monetary expansion," President Dilma Rousseff said.
China, holder of the world's largest foreign exchange reserves, will contribute the bulk of the contingency currency pool, or $41 billion. Brazil, India and Russia will chip in $18 billion each and South Africa $5 billion.
If a need arises, China will be eligible to ask for half of its contribution, South Africa for double and the remaining countries the amount they put in.
Negotiations over the headquarters and first presidency were reached at the eleventh hour due to differences between India and China. The impasse reflected the difficulties that Brazil, Russia, India, China and South Africa face in working together to build an alternative to the Bretton Woods institutions dominated by the International Monetary Fund and the World Bank.
"We pulled it off 10 minutes before the end of the game. We reached a balanced package that is satisfactory to all," a Brazilian diplomat told Reuters.
Negotiations to create the bank dragged on for more than two years as Brazil and India fought China's attempts to get a bigger share in the lender than the others.
Stark economic and political differences between the BRICS countries have made it difficult for the group to turn rhetoric into concrete action in coordinating policies.