A review of his fund-raising practices by The New York Times earlier this year showed that he has pushed the boundaries of campaign-finance and ethics laws, though he has not been formally accused of wrongdoing. And the last month of the campaign saw controversies over transparency issues play out concerning his tax and real estate disclosures and even questions of residency, culminating in an extraordinary moment in which Mr. Adams offered journalists a tour of the apartment where he said he lived.
Mr. Adams’s formative years in the public eye were spent in the Police Department, where he helped found an organization called 100 Blacks in Law Enforcement Who Care. His efforts inspired some and rankled other colleagues on the force who describe a career trajectory that was more complex than Mr. Adams sometimes suggests.
But to this day, some voters remember Mr. Adams from those efforts, which helped him dispatch arguments from opponents that he was overly inclined to embrace policing as an answer to the city’s challenges.
“My admiration for him really started when he was a policeman talking about police brutality, and a captain talking about police officers not fulfilling their oath,” said Charles B. Rangel, the former New York congressman, who endorsed Mr. Adams.
As an outspoken police officer, Mr. Adams had his share of controversies, too, aligning himself at various times with Louis Farrakhan, the Nation of Islam leader who has repeatedly promoted anti-Semitism, and the ex-boxer Mike Tyson after his 1992 rape conviction. Mr. Adams lost a 1994 congressional run, and he was also a registered Republican for a period of time in the 1990s.
In 2006, he was elected to the State Senate as a Democrat, part of a wave of Central Brooklyn politicians who came up from outside the party, and in 2013, won an election to be Brooklyn borough president.
Mr. Adams, who became an evangelist for veganism after he says he reversed his diabetes by reforming his diet and exercise routines, became known for preparing vegan meals at Borough Hall, and he developed a reputation as a splashy New York character prone to making unexpected remarks and appearances. There was the gruesome rat-related news conference, for instance, or Mr. Adams’s announcement that he, as a former law enforcement officer, would begin bringing a gun to houses of worship after a massacre in a Pittsburgh synagogue.