Koch's spokesman, George Arzt, said the former mayor died of congestive heart failure at New York-Presbyterian Columbia Hospital, where was being treated, The New York Times reported.
Koch had coronary and other medical problems since he left office in 1989, but had always been in relatively good health in his on-the-go life as a television judge, radio talk-show host, author, lawyer, newspaper columnist and professor, among other pursuits.
The premiere of "Koch," a documentary biographical film, was opening Friday nationwide.
His 12-year tenure as mayor encompassed the fiscal austerity of the late 1970s and the racial conflicts and corruption scandals of the 1980s.
He is credited with steering the city government from near bankruptcy in the 1970s to prosperity in the 1980s, the Times said. He also began one of New York's most ambitious housing programs, which continued after he left office and eventually built or rehabilitated more than 200,000 housing units.
"I'm the sort of person who will never get ulcers," the mayor told reporters on Inauguration Day in 1978. "Why? Because I say exactly what I think. I'm the sort of person who might give other people ulcers."
Koch shifted from an independent liberal to pragmatic conservative on the Democratic spectrum during his political life that included serving two years as a councilman and nine more in Congress representing Manhattan's East Side.
The gregarious, media-conscious Koch -- known for his catch phrase "How'm I doin'?" -- courted comparison with the legendary reform politician Fiorello La Guardia, the only other three-term New York mayor, who ran the city from the Depression through World War II.
Koch won national recognition as the combative symbol of the city he served. But he was buffeted by a series of political scandals after his election to a third term in 1985, beginning in March 1986 with the gruesome suicide of a political ally, the Democratic boss of Queens, Donald Manes.
The scandal began with the city's Parking Violations Bureau and spread to include the Taxi and Limousine Commission, Transportation Department, and several of Koch's commissioners and top aides.
Koch was not directly implicated in the scandal and maintained he was unaware of the crimes being committed around him. But he conceded his alliance with the Democratic Party bosses to get elected to a first term and then win legislative support in Albany during the city's fiscal crisis gave the leaders access to his commissioners.
In November 1986, former Bronx Democratic leader Stanley Friedman was convicted of using the city's Parking Violations Bureau for personal profit and of paying pay bribes to Manes.
In April 1987, another Koch ally and dinner companion, former Miss America Bess Myerson, resigned as the city's cultural affairs commissioner amid charges she used her position to influence a judge.
The once seemingly invincible Koch took only one stab at higher office, entering the Democratic race for governor in 1982 as the heavy favorite after his landslide re-election as mayor in 1981.
Although he had what appeared to be overwhelming financial backing from corporations and real estate moguls, he lost a stunning defeat to Mario Cuomo, whom Koch had beaten in the mayoral race five years earlier.
In 1989, Koch was defeated by David Dinkins, who went on to become New York's first black mayor.
Koch's political career was built on contradictions. He entered politics in opposition to political bosses, but as mayor he gave the bosses such access to City Hall they virtually took over several of his departments.
He won his third term in 1985 with a record 75 percent of the vote while also setting a record for spending the most on a campaign $7.5 million. The campaign set another mark for lowest turnout ever when only 31 percent of the city's voters went to the polls.
As a young lawyer, Koch went to Birmingham, Ala., with the freedom riders, but his tenure in Gracie Mansion was marked by continual sparring with the city's black community whose leaders accused him of insensitivity to their needs.
In February 1986, he appointed Benjamin Ward as New York's first black police commissioner, later standing by him when Ward himself was criticized for statements that his opponents called racially and sexually insensitive.
Koch wrote a best-selling book, "Mayor," and followed it with one titled "Politics," but refused to cooperate with an unauthorized and critical biography titled "I, Koch."
The son of Polish immigrants, Koch developed rich tastes as mayor and was linked with the city's wealthiest and most powerful developers.
He was a media gadfly who rarely refused an interview, and appeared in so many bit parts on Broadway, television and music videos he joined the actors union.
The tall, balding, bachelor mayor was witty, whiney, tight-fisted, sharped-tongued, combative and New Yorkers loved it. He pressed the point repeatedly in public, booming out the question, "How'm I doing?" or with the jibe, "I'll get a better job, but you won't get a better mayor."
Koch made his first run for mayor in 1973 but dropped out for lack of support. In 1977 he won the office after taking the Democratic Party nomination away from incumbent Abraham Beame.
Koch was known for his optimism, especially in tackling New York City's staggering budget deficits, union demands and other problems of city government. He said he did his best to revive New York City's bruised spirit -- the city budget was $295 million in the red when he came into office.
Koch was born in the Bronx on Dec. 12, 1924. His parents came from Poland when they were 14 and lived in the lower East Side.
In 1943, Koch joined the Army. He rose to the rank of sergeant in the infantry and in Bavaria he became a de-Nazification specialist. After the end of World War II, Koch graduated from New York University law school and went into practice.
He moved to Greenwich Village in 1956 and got his first taste of politics on the street corners when he spoke out for Adlai Stevenson, the Democratic Party's candidate for president against Republican Dwight D. Eisenhower.
In 1962, Koch became a charter member of the Village Democrats and the party ran him against Assemblyman William Passannante. The election was a horrible loss for Koch. He vowed he would "never run for anything again."
Koch, a lifelong bachelor, is survived by his sister, Pat, a former dean at New York University. His brother, Harold, died in 1995.