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Mr. Goldsmith, a former mayor of Indianapolis, was brought in by Mr. Bloomberg last year with much fanfare: a Harvard professor and expert in innovation poached from the ivory tower to reinvent city government.

But Mr. Goldsmith never seemed to master the day-to-day mechanics of New York’s sprawling government or relish the political intricacies of the job, and dissatisfaction with his performance became widespread in City Hall, according to two aides to Mr. Bloomberg who spoke on the condition of anonymity for fear of angering the mayor.

Mr. Goldsmith informed Mr. Bloomberg of his resignation this week. He is being replaced by Caswell F. Holloway, the commissioner of the city’s Department of Environmental Protection.

The departure is another setback for the mayor’s effort to bring fresh-faced outsiders — like Mr. Goldsmith and the publishing executive Cathleen P. Black, who briefly served as schools chancellor — into his administration to energize his third term.

In a statement, Mr. Goldsmith said he was leaving the administration to return to academic work and to pursue opportunities in the financial sector, though he has not yet lined up a job. Friends described his resignation as abrupt; he had been scheduling meetings and discussing policy proposals as recently as last week.

Mr. Goldsmith did not respond to interview requests on Thursday. “The change will provide me, at age 64, with more flexibility for me and my family and a secure foundation for our future,” he said in the statement.

Mr. Goldsmith, like Ms. Black, was seen by Mr. Bloomberg as a bold choice who could help shape what has seemed at times to be an unfocused third term. Instead, both of them clashed with those they supervised, struggled to master their jobs and became the subject of open sniping in City Hall.

Mr. Goldsmith’s position, as deputy mayor of operations, made him responsible for the city agencies by which New Yorkers measure the efficiency of their government: police, fire, transportation, sanitation and buildings.

His most visible moment on the job was also perhaps his lowest: he became the face of the city’s lackluster response to the Dec. 26 snowstorm. Many of the top city officials, including Mr. Bloomberg, were out of town during the storm. Mr. Goldsmith had been at his home in the Georgetown section of Washington, and on the evening of the snowstorm, he posted a message on his Twitter feed praising city workers, which many snowbound New Yorkers saw as out of touch. “Good snow work,” he wrote.

At a raucous City Council hearing after the blizzard, Mr. Goldsmith apologized several times and acknowledged wide-ranging mistakes.

From the day he took office in June 2010, Mr. Goldsmith, who regarded himself as a management guru but knew little about New York’s vast bureaucracy, repeatedly frustrated his colleagues, according to interviews with City Hall aides and advisers.

In his first major labor move, Mr. Goldsmith overruled the advice of some longtime city officials by announcing plans to demote 100 supervisors from the Sanitation Department and return them to the front lines.

The decision had two immediate consequences. It infuriated the head of the sanitation workers union, Harry Nespoli, who, as the leader of the powerful Municipal Labor Council, plays a crucial role in the city’s labor relations. And it angered the work force responsible for clearing snow just weeks before the blizzard.

Mr. Nespoli said Mr. Goldsmith had failed to listen to his warnings about low staffing levels and morale in the Sanitation Department. “You don’t come in and say, ‘I was in Indianapolis, and this is what we did there,’ ” he said. “That doesn’t work in New York.”

City Hall aides complained that, in meetings, Mr. Goldsmith emphasized management theory over political pragmatism. As a result, they said, conversations devolved at times into convoluted academic discussions that resolved little.

When City Hall staff members met to discuss the growing public outcry over the reconstruction of a major roadway in the Bronx, which was hurting beloved local trees, Mr. Goldsmith engaged in a discourse about eliminating risk in government. Those in the room were befuddled, according to people with knowledge of the meeting.