Moore, a well-known and often polarizing figure in Washington political circles, served as an adviser to Trump during the 2016 campaign. In that role, he helped draft Trump's tax cut plan.
Trump has been harshly critical of the Fed's rate increases even after the central bank announced this week that it foresees no hikes this year. Moore, formerly chief economist for the conservative Heritage Foundation, has also been critical of the policies of Chairman Jerome Powell.
A fervent advocate of tax cuts, Moore is close to Larry Kudlow, head of the White House National Economic Council. The two collaborated in shaping the tax overhaul that Trump signed into law at the end of 2017, leading to changes that largely favored tax cuts for corporations and wealthier individuals with the idea of spurring investment and growth.
Moore, interviewed Friday on Bloomberg television after Trump's announcement, said his criticism of the Fed, including his suggestion that Powell should perhaps be fired, were "probably written in a time of anger."
"I think everyone would now acknowledge," Moore added, "that what they did in December with the rate increase was a very substantial mistake. And the Fed has, thank God, reversed that and changed directions."
Asked whether Trump might want him on the Fed's board to check Powell's influence and protect the administration's economic policies, Moore said, "The only thing (Trump) told me was, pursue policies that are good for the American workers. ... He didn't really mention anything about differing with Chairman Powell one way or the other."
Moore's nomination, which the Senate must confirm, drew sharp criticism from some economists and historians.
"It's unprecedented in the modern era, particularly because he lacks expertise in areas under the Fed's supervision, like banking and monetary policy," said Gary Richardson, a historian of the Fed and a professor at the University of California at Irvine.
Scott Sumner, the chair of monetary policy at George Mason University's Mercatus Center, said his concern is that Moore accused the Fed of providing too much aid after the 2008 financial crisis, when the economy depended on help from the central bank. Moore has since urged the Fed to be more generous in supporting the economy, even though growth has strengthened in the past two years and less help is needed.
"His policies appear to be going the wrong way," Sumner said.
Given his sharply partisan reputation, Moore could spark opposition among Democrats in the Senate. But Trump can score points with his core supporters — and with the majority Republicans in the Senate — by embracing a conservative activist for a Fed role that would make him a watchdog over the economy.
"FreedomWorks is proud to see President Trump offer such a prestigious position to one of our own," said Adam Brandon, president of that conservative advocacy group. "I have no doubt that Stephen Moore would make an excellent member of the Federal Reserve Board."
Trump in his first two years in office has been able to reshape the central bank. He nominated four of the current five members. And he tapped Powell, who had been chosen for the Fed board by President Barack Obama, to succeed Janet Yellen as chairman. If confirmed by the Senate, Moore would fill one of two vacancies on the board.
The selection of Moore marks a deviation from Trump's previous choices for the board, toward a more public figure who has long pushed conservative economic and political ideology.
In a March editorial in The Wall Street Journal, Moore estimated that Fed rate policies had reduced inflation-adjusted economic growth by as much as 1.5 percentage points in the past six months. Moore proposed that the Fed set short-term rates with an eye toward stabilizing commodity prices, rather than solely on overall inflation.
This approach, Moore has argued, would have prevented the Fed from raising rates as much as it has. And he contended that this approach, if adopted, would help accelerate economic growth above 3 percent, compared with the longer-run average of 1.9 percent that Fed officials have forecast.
Moore has often embraced a confrontational tone in his commentary on the Fed. In a 2012 Wall Street Journal column, he suggested that the chairman at the time, Ben Bernanke, had kept rates near zero and arranged for the Fed to buy bonds in order to help Barack Obama win re-election, rather than help the economy recover from the financial crisis and Great Recession.
Moore had earlier predicted in 2010 that the Fed's low rates would ignite inflation, and he advised investors to buy gold. He pressed his case in 2011, warning on Fox News, "We're starting to see that specter of inflation."
His warnings of runaway inflation proved off-base. The average inflation rate would fall from 3.1 percent in 2011 to near zero in 2015.
With Trump as president, Moore became a sharp critic of Fed policies to shrink its balance sheet and return rates to what the central bank sees as a neutral level — neither stimulating nor hindering growth. He went so far as to suggest that Trump might consider trying to fire Powell for the rate hikes under his watch.
"What the law says, I believe, is (Trump) can replace the Federal Reserve Chairman for cause," Moore said during a December radio interview. "And, you know, I would say, well, the cause is that he's wrecking our economy."
Moore has frequently praised the administration on television, and he co-wrote the 2018 book "Trumponomics." His partner on that book was Art Laffer, who pioneered the Republican doctrine that lower tax rates would accelerate economic growth in ways that could minimize debt.
But federal debt has jumped since Trump's overhaul to the tax code, surging nearly 77 percent through the first four months of fiscal 2019 compared with the previous year.
AP staff writers Deb Riechman and Marcy Gordon contributed to this report.