In a memo to the consumer watchdog's employees, Cordray said his current chief of staff, Leandra English, would become deputy director and automatically rise to acting director when he leaves.
"The president looks forward to seeing Director Mulvaney take a common sense approach to leading the CFPB's dedicated staff, an approach that will empower consumers to make their own financial decisions and facilitate investment in our communities", the White House said in its statement.
In his resignation letter Friday, Cordray said that the agency "has stood on the side of consumers to see that they are treated fairly, worked to improve their financial situations and held financial institutions accountable". Students, veterans, and military families in particular have benefited from a strong CFPB under director Cordray.
Director Richard Cordray says that he is leaving the agency Friday after announcing his plans to resign several weeks ago.
Earlier this month, White House deputy press secretary Raj Shah said that the administration "will announce an acting director and the president's choice to replace Mr Cordray at the appropriate time". But there is debate over how much authority Cordray has to appoint his replacement. "It puts attention where it should be, which is on the White House formally nominating someone and going through the process".
However, the White House had already said it planned to name its own interim leadership at the regulator.
The CFPB was established as part of Dodd-Frank after the financial crisis to police credit cards, auto loans and other consumer-finance products.
The vote was criticised by many Democrats as a sop to Wall Street. English had been serving as the Obama-era agency's chief of staff. The head of the agency serves for five years and can only be ousted for cause. In addition to her work at the CFPB, Ms.