The Biden administration saw a key figure of its financial-regulatory team move into place as the Senate confirmed Michael Barr to become the government’s most influential banking regulator.

Mr. Barr’s confirmation Wednesday as the Federal Reserve’s vice chairman for supervision provides the central bank with a full seven-member board for the first time in nearly a decade and adds to a group of Biden-appointed bank overseers who may revisit financial regulations that were eased during the Trump administration.