Dr. Howard’s decision represented an about-face from assurances by the federal government immediately after the terrorist attacks that there was nothing in the air to be worried about. In July 2011, Dr. Howard himself said there was not enough scientific or medical evidence to link cancer to Sept. 11.

But in a lengthy report explaining his decision, Dr. Howard said that a New York Fire Department study published last fall in the British medical journal The Lancet, which showed that firefighters exposed to ground zero toxic substances had about 20 percent higher rate of cancer than firefighters who were not exposed, had provided a strong foundation for a conclusion that some cancers had been caused by exposure to the World Trade Center debris.

Beyond the Lancet study, he said, he had relied on recommendations made in late March by a scientific and technical advisory committee consisting of experts from the fields of cancer, environmental medicine, toxicology and epidemiology as well as neighborhood activists and union officials. He fully adopted the committee’s recommendation that 14 broad categories of cancer, encompassing 50 specific types, should be deemed as related to the attacks.

Among the cancers Dr. Howard approved are some of the most common, including lung, breast, colon, trachea, esophageal, kidney, bladder, skin, thyroid, blood and ovarian cancers. Dr. Howard also approved childhood cancers, which are relatively rare, because children are more susceptible to toxic substances.

People with covered cancers who lived, worked or attended school in Lower Manhattan — generally the area below Canal Street — between Sept. 11, 2001, and May 30, 2002, would be able to apply for compensation for their economic losses, pain and suffering. Until the decision on Friday, the only ailments approved for compensation were mainly respiratory and digestive ones. Survivors of patients who have died, as well as people caught in the dust cloud downtown on the day of the attack, may also apply.

The amount of compensation will depend on the severity of the illness and duration of exposure, as proven by records like employment or housing documents, or city personnel records for fire, police and other public workers.

The new rules would apply to Pentagon and Shanksville, Pa., responders as well, and it allows those cancer patients to tap into a treatment fund to pay for medical costs not covered by insurance.