Quarles, 60, who served as undersecretary of the Treasury under former President George W Bush and previously worked in private equity, was confirmed by a vote of 65 to 32.
As a Fed governor, he will also sit on the Federal Open Market Committee, which sets US monetary policy.
As President Donald Trump's first Fed nominee, Quarles will oversee banking regulation at a time when the White House has sought to scrap many of the rules put in place following the 2008 financial meltdown.
Quarles has been critical of the regulatory burden imposed on larger banks deemed "too big to fail," or so important to the financial system their failure would endanger the broader economy.
In particular, Quarles wrote in 2016 that raising banking reserve requirements was tantamount to raising the cost of borrowing.
With next week's departure of Fed Vice Chair Stanley Fischer, Trump will have three vacancies to fill at the central bank.
"I think it's very important to have a broad range of views around the table as we deliberate on policy actions," Yellen said.
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