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 US Senate has adopted long-awaited reforms to give emerging economies a greater say in how the International Monetary Fund (IMF) is managed.