Janet Yellen will join the ranks of the most powerful economic policy makers in the world next month, taking the helm of the Federal Reserve at a time when the central bank is assessing its unprecedented steps to buoy the U.S. economy.

The 67-year-old Ms. Yellen, currently the vice chairwoman of the Fed's board of governors, will become the first woman to lead the central bank in its 100-year history after the Senate voted to confirm her Monday night in a 56-26 vote. Eleven Republicans joined 45 Democrats to support her;...