The decision, announced after financial markets closed, gives Biden a pair of trusted Washington insiders to steer economic policy as the risk of recession fades but inflation lingers.
Big fights also loom with the Republican-controlled House of Representatives over raising the debt ceiling.
The shakeup comes as the White House tries to tackle what officials view as a frustrating disconnect between relatively strong economic data and weak public sentiment.
The White House has refused to discuss spending cuts without a debt ceiling vote first.
Bernstein last week conceded that the White House's early description of inflation as "transitory" had missed the mark.