China's voting rights will rise to 6%, from 3.8% and IMF resources will double to about $660bn (Â£440bn).
This is the biggest shake-up since the IMF and the World Bank were set up to manage the post-World War Two economy.
China has set up the Asian Infrastructure Investment Bank as an alternative to the IMF and the WB.
The IMF reforms were agreed by its 188 members in the aftermath of the world financial crisis in 2010.
As China's voting rights rise, the US will see its share drop from 16.7% to 16.5%. The US also retains its veto power.
India's voting rights will rise to 2.6% from the current 2.3%.
The biggest losers are European economies which will see their voting rights diminished.
The US was behind the initiative to bring in the 2010 reforms in a bid to keep China happy.
But Republicans in the US Congress had been concerned at the diminishing US influence.
US Treasury Secretary Jacob Lew said in a statement: "The IMF reforms reinforce the central leadership role of the United States  in the global economic system and demonstrate our commitment to maintaining  that position."
IMF chief Christine Lagarde hailed the US adoption as a "a welcome and crucial step forward that will strengthen the IMF in its role of supporting  global financial stability".
And China's Central Bank said the reform "will improve the representation and voice of emerging markets and developing countries in the IMF and is conducive to protecting the IMF's credibility, legitimacy and effectiveness".
Last month, the IMF decided to include China's currency, the renminbi, as a reserve currency, alongside the US dollar, the euro, the yen and the British pound.
The IMF and the WB were conceived in 1944 at a conference in Bretton Woods, in the US state of New Hampshire.
The IMF aims to preserve economic stability and to tackle - or ideally prevent - financial crises. Over time, its focus has switched to the developing world.
The WB is the world's leading development organisation, working for growth and poverty reduction.

The All Nippon Airlines (ANA) flight will take off from Tokyo around 1230 local time, bound for Hong Kong.
The Dreamliner had originally been scheduled for delivery in 2008, but Boeing has suffered a string of setbacks.
Boeing plans to make 10 of the planes a month from 2013.
Wednesday's flight is a special charter, with normal services due to start in November.
Because of the materials used in construction, Boeing says the Dreamliner is about 20% more fuel efficient than similarly sized models flying today.
That would be a big help for airlines coping with the high cost of jet fuel, which is usually their biggest single cost.
Japan, a country in which Boeing dominates rival Airbus, is a major market for the Dreamliner.
ANA will take delivery of dozens more of the aircraft in the coming years.
But Boeing's delays have hurt its business.
Last week, China Eastern Airlines cancelled orders for 24 Dreamliners, rather than wait for production to pick up.

The League Two newcomers fell behind on 27 minutes when Joshua Mullin headed in a free-kick from Nicky Cadden.
Mullin then provided a neat cross for Daniel Mullen to knock in right on the stroke of half time.
Mikey Miller crashed a shot against the woodwork as the visitors from League One continued to dominate before Liam Buchanan made it 3-0 from close range.
Ousman See went close for the hosts but was denied a landmark goal by a smart save from Liam Kelly.
Livingston move up to second place in Group G, behind St Mirren, who have two wins from two.
The US Senate has adopted long-awaited reforms to give emerging economies a greater say in how the International Monetary Fund (IMF) is managed.
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After three years of delays, Boeing's Dreamliner jet is set for its maiden commercial voyage.
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Edinburgh City's first competitive match as an SPFL side ended in League Cup defeat to Livingston at Meadowbank.