Waller, who is also an economics scholar, and Shelton will have to be confirmed by the US Senate before they can join the seven-member governing board of the nation's central bank. If confirmed, they would serve 14-year terms.
Before joining the St. Louis branch of the Federal Reserve Bank in 2009, Waller chaired the economics department at the University of Notre Dame and had a long career as a professor and research fellow at various think tanks and universities. According to the St. Louis bank's website, "his principal research interests are monetary theory, political economy and macroeconomic theory."
Trump also announced his nomination of Shelton, one of his economic advisers with a known penchant for criticizing the Federal Reserve.
In May, Shelton told the New York Times that Fed’s practice of paying interest on excess money that banks keep at the Fed was "like paying the banks to do nothing." She said it discourages lending of money and that she favors reducing interest rates to zero - something Trump has also criticized the bank for failing to do.
Trump floated several other candidates earlier this year, including Herman Cain and Stephen Moore, both of whom were withdrawn from consideration after lawmakers made it clear they wouldn't support the candidates. Two others, Nellie Liang and Marvin Goodfriend, were formally nominated but rejected by the Senate.
Last month, Trump reportedly indicated he believes he has the power to remove Federal Reserve Chair Jerome Powell, whose term as chairman doesn't expire until 2022.
The Federal Reserve governs the US financial system, with its primary focus being monetary policy, with the aim of avoiding or mitigating financial crises. Unlike most other countries' central banks, the Federal Reserve doesn't print money - the US Treasury does. Rather, the Federal Reserve serves as a bank for banks, mandating they keep some of their reserves in its vaults - as well as a certain percentage of their total holdings in their own vaults - and lending banks money as a last resort, when its economists deem it necessary to stabilize the economy. It also moderates interest rates.