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7 year oldYadira Arroyo, 44, was responding to a call with another paramedic in the Bronx neighbourhood on Thursday night when she was hit.
Authorities charged Jose Gonzalez, 25, with murder, grand larceny and driving while impaired by drugs.
Ms Arroyo was a mother of five children and a 14-year fire department veteran.
The two paramedics were told a man was riding on the back bumper of their ambulance when they stopped to check, according to Fire Commissioner Daniel Nigro.
Mr Gonzalez went around to the other side of the vehicle and got into the driver's seat.
He then put the ambulance in reverse and hit Ms Arroyo, who was caught beneath the wheels.
The second unidentified female paramedic was still in the passenger seat when the vehicle was being stolen. She was treated in hospital for minor injuries, police said.
Footage of the incident emerged on Twitter of the incident, showing the ambulance crossing an intersection with one of its doors open and the body of one of the paramedics being dragged beneath the vehicle.
The ambulance then crashed into several parked cars before it came to a halt on a snowbank.
A Metropolitan Transportation Authority K-9 officer and another bystander then apprehended Mr Gonzalez.
"They were acting very bravely. They certainly wanted to continue on their way to the call. This person had no business being in this ambulance," Mr Nigro said.
New York Mayor Bill de Blasio praised the "good Samaritans" who helped out.
"A lot of heroism was on display amidst a great tragedy," he said.
Governor Andrew Cuomo said paramedics are "heroes who help countless New Yorkers every day. Tonight's tragedy in the Bronx is horrible. My deepest sympathies to the family".
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