The incident, which police say happened without warning, took place on a commercial strip of Jamaica Avenue and 162nd Street around 2 p.m.
Tap/click here to see video of the man the moment before the attack.
NYPD Commissioner William Bratton said a group of four rookie uniformed officers were on patrol as part of the NYPD Operation Impact initiative when a freelance photographer asked them to stand for a photograph.
They were standing near the corner when the assailant, 32-year-old Zale Thompson, approached them and started swinging the hatchet without uttering a word. One officer, 25-year old Kenneth Healey, was struck in the head, while a second, 24-year old Joseph Meeker, was struck in the arm.
The other two officers, who suffered minor injuries, opened fire on the hatchet-wielding man.
"As he continued his assault, the remaining two officers then fired multiple times on the armed suspect, who fell to the ground dropping the hatchet. The suspect was pronounced dead at the scene," said Bratton.
The most seriously injured officer was rushed to Jamaica Medical Center, where he is listed in critical but stable condition after undergoing surgery. The second injured officer was also hospitalized, while another was being treated for trauma at North Shore University Hospital.
A female bystander, 29, was struck in the lower back by the gunfire. She was rushed to Jamaica Medical Center, where she underwent surgery. She is also in critical but stable condition.
Both officers were reportedly conscious and alert while being transported.
Witnesses said the suspect was arguing with a woman prior to the incident.
Zale Thompson had a long history filled with what sources describe as hate speech aimed at what he apparently saw as the white government power structure in America, suggesting it was time to rise up in opposition.
Some sections do appear inspired by Islamist ideas, sources said, though they do not believe he was solely inspired by ISIS.
At his news conference, Bratton held up a picture of the hatchet he said was used in the attack, approximately 18 inches and a half inches long.
He was asked about a possible terrorist connection in light of Wednesday's shooting of a soldier in Canada, and said it could not be ruled out.
"The heightened concerns relative to that type of assault based on what's just happened in Canada and recent events in Israel are certainly one of the things that first comes to mind, but that's what the investigation will attempt to determine," Bratton said.
The freelance photographer is providing police with photos of the incident as part of the investigation.