In an announcement at the White House's Rose Garden on Thursday, Trump praised Powell's "hard work, expertise and judgment" to head the agency, which sets the monetary policy of the US and monitors the banking system.
"He is proven to be a consensus builder for the sound, monetary and financial policy that he so strongly believes in," Trump said.
"Based on his record, I am confident that [he] has the wisdom and leadership to guide our economy through any challenges that our great economy may face."
In accepting the nomination, Powell said he would "do everything" in his power to fulfil his role of making prices stable and maximise employment.
"In the years since the global financial crisis ended, our economy has made substantial progress towards full recovery. By many measures, we are close to full employment; inflation has gradually moved up toward our target," he said.
He also said that the country's financial situation is "far stronger and more resilient" than it was during the crisis in 2008.
Before the announcement, Powell served as a member of the Board of Governors of the Federal Reserve.
A registered Republican, he was appointed to his board position in 2012 by Democratic President Barack Obama.
Powell had also served as an undersecretary of the US Department of Treasury, and several private financial institutions, including the Global Environment Fund, a private equity firm that invests in sustainable energy.
Powell, a multimillionaire, was seen as a safe pick by Trump, and the US markets and dollar index remained steady as the announcement was made.
According to a Bloomberg News analysis, Powell's personal wealth could be worth as much as $112.3m, making him "the wealthiest Federal Reserve chairman in decades".
With the unemployment rate at its lowest in 16 years and the economy growing, Powell is expected to maintain the policy of his predecessor.
If confirmed by the Republican-controlled Senate, Powell will start his term in February 2018, serving at least one four-year term.
By appointing Powell, Trump broke with decades-old tradition observed by previous presidents of re-appointing the chairman of the Federal Reserve.
Yellen was appointed by Obama in 2013 and started her term in 2014.