The next president of the New York Fed will also take Mr. Dudley’s place as the vice chairman and a permanent voting member of the Federal Open Market Committee, which sets the Federal Reserve’s policy decisions about interest rates and the purchase and sale of securities on the open market. Mr. Dudley has voted in favor of the Fed’s current approach to monetary policy.

In a speech last month, Mr. Dudley said that while he remained puzzled about why inflation had yet to meet the Fed’s longer-run objective of 2 percent, he believed that raising rates slowly continued to be the right path.

“I expect inflation will rise and stabilize around the F.O.M.C.’s 2 percent objective over the medium term,” he said. “Thus, even though inflation is currently somewhat below our longer-run objective, I judge that it is still appropriate to continue to remove monetary policy accommodation gradually.”

He is expected to retire sometime this spring, the two people familiar with the decision said, and a search is underway for his successor. The people spoke on the condition of anonymity because they were not authorized to discuss Mr. Dudley’s decision publicly. CNBC earlier reported Mr. Dudley’s plans.

Unlike the Fed chairman, regional Fed bank presidents are not political appointees and are not chosen by the president. They are selected by a committee composed of members of the Fed’s board of directors who are not affiliated with financial institutions, and the selection is subject to approval by the Fed board in Washington.