Warsh, 56, a former top Fed official, was confirmed Wednesday in a largely party-line 54-45 vote and will replace Jerome Powell as chair at an unusually difficult time for the independent agency.
Inflation has topped the Fed's 2.0 per cent target for five years and is now rising faster because of spiking gas prices.
The Fed's interest rate-setting committee is divided and saw the most dissenting votes in more than three decades last month.
And Powell, after years of personal attacks from Trump and an unprecedented Justice Department investigation, plans to remain on the Fed's board even after his term as chair ends, potentially creating a competing power centre.
Senate Majority Leader John Thune said in a floor speech that it's critical that a Fed chair "understand not only the macro" but also "appreciate the microeconomy: and that's the hardworking Americans, their jobs and their livelihoods".
"Kevin Warsh is just such a person," Thune said.
The Fed has faced threats to its independence from Trump, who has repeatedly attacked Powell for not cutting interest rates.
Trump also sought to fire Fed governor Lisa Cook and launched an investigation into Powell's Senate testimony about a building renovation.
The probe of Powell had threatened to derail Warsh's nomination, as Republican Senator Thom Tillis of North Carolina vowed to withhold support until the investigation was terminated.
The probe was ultimately dropped in April.
Every Republican voted for Warsh on Wednesday, as did Democratic Senator John Fetterman of Pennsylvania.
Kevin Hassett, director of the White House's National Economic Council, said in a Fox News interview on Sunday that he believes the markets are relieved that Warsh "is going to help lower interest rates over time".
"Obviously, data-driven," said Hassett.
"I'm not putting any pressure on Kevin Warsh."
In December, Trump said on his social media platform that he wanted a Fed chair who would cut interest rates when the stock market rose — the opposite of what traditional economics would prescribe.
"Anyone that disagrees with me will never be the Fed chairman!" he said.
Trump's comments have fuelled concerns over whether Warsh will set rates based on economic conditions or instead seek to appease Trump, even if doing so could worsen inflation.
At Warsh's confirmation hearing last month, Senator Elizabeth Warren, a Democrat from Massachusetts, derided him as a "sock puppet" for Trump.
Still, Warsh denied at the hearing that Trump had pressured him to reduce the Fed's key rate.
"I will be an independent actor if confirmed as chair of the Federal Reserve," he said.
Warsh has been highly critical of the Fed's recent track record, particularly the inflation spike in 2021-22, the worst in four decades.
He has called for limiting the Fed's communications, which would be a sharp shift after decades of growing transparency.
He has argued that some of its communications tools, such as quarterly forecasts of where its key rate may head, have made it harder for officials to switch gears.
Senate Democrats have also condemned Warsh for not fully divulging the details of his wealth, which amounts to at least $US100 million ($A138 million).
His investments include stakes in Polymarket and SpaceX, but he hasn't revealed the size of those holdings. He promised to sell all such assets within 90 days of being sworn in.
"He will be the wealthiest Fed chair in history, but he refuses to provide transparency to the American people about who he is entangled with," Warren said.
Warsh faces difficult economic conditions.
The Fed is still grappling with how to respond to the 50 per cent spike in gas prices caused by the war in Iran.
The increase has boosted inflation, which reached 3.8 per cent in April.
