Warsh would replace current chair Jerome Powell when his term expires in May. Trump chose Powell to lead the Fed in 2017 but this year has relentlessly assailed him for not cutting interest rates quickly enough.
"I have known Kevin for a long period of time, and have no doubt that he will go down as one of the GREAT Fed Chairmen, maybe the best," Trump posted on his Truth Social site.
"On top of everything else, he is 'central casting,' and he will never let you down."
The appointment, which requires Senate confirmation, amounts to a return trip for Warsh, 55, who was a member of the Fed's board from 2006 to 2011.
He was the youngest governor in history when he was appointed at age 35. He is currently a fellow at the right-leaning Hoover Institution and a lecturer at the Stanford Graduate School of Business.
In some ways, Warsh is an unlikely choice for the Republican president because he has long been a hawk in Fed parlance, or someone who typically supports higher interest rates to control inflation. Trump has said the Fed's key rate should be as low as one per cent, far below its current level of about 3.6 per cent, a stance few economists endorse.
During his time as governor, Warsh objected to some of the low-interest rate policies that the Fed pursued during and after the 2008-09 Great Recession. He also often expressed concern at that time that inflation would soon accelerate, even though it remained at rock-bottom levels for many years after that recession ended.
But more recently, however, in speeches and opinion columns, Warsh has said he supports lower rates.
In his first term, President Trump passed over Warsh in favour of Powell, a choice he regretted when Powell would not cut interest rates as fast or deep as Trump urged.
This time around Trump made support for lower rates one of his explicit criteria for a Fed chair candidate.
Trump's nomination of a Powell successor, who must be confirmed by the Senate, comes amid unprecedented presidential efforts to exert control over the Fed. Traditionally, the independence of the central bank from political pressure has been seen as key to its job to fight inflation.
Trump's efforts include an attempt to oust Fed Governor Lisa Cook in a case now before the Supreme Court, and a Department of Justice probe that Powell says is part of a broad attempt by the administration to intimidate the Fed.
Powell's chair term ends in May, and he has declined to say if he will take the unusual step of staying on as a Fed governor.
Powell's term as a member of the Board of Governors expires in 2028.
with AP
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