The settlement between the utility company Con Edison and the family of Jodie Lane came 10 months after the 30-year-old doctoral student died in the East Village after falling onto an electrified metal plate while walking her dogs.
The dogs started fighting and as she tried to separate them she slipped on the icy ground and landed on the manhole cover.
The plate had become electrified because of a poorly insulated wire in a utility box and carried the charge above ground with the help of salt that had been used to grit the roads.
When the emergency services arrived they did not touch Ms Lane for fear that they too would be electrocuted. One officer suffered an electric shock when she came too close.
The public and tragic circumstances of her death led to strong criticism of Con Edison, leading to new safety rules and more rigorous inspections of electrical equipment. The mayor of New York, Michael Bloomberg criticised Con Edison for its "unacceptable" maintenance of power lines.
"It's just unacceptable that somebody can walk on a street and get electrocuted and we've got to make sure that doesn't happen again," he said.
As well as the compensation for the Lane family the settlement includes $1m for Columbia University's Teachers College for scholarships and research in the clinical psychology department, where Ms Lane was studying.
Con Edison also agreed to provide two members of a three-person panel that will periodically review its safety procedures.
The Lane family is to set up a foundation that will provide the third panel member.
"A settlement like this is never easy to achieve," Ms Lane's father, Roger Lane, told the New York Times.
"But I think the parties to the settlement acted in a first-class manner and the end result is something quite unusual."
According to court papers filed in Manhattan on Tuesday, from the $6.25m settlement $5.27m was for wrongful death and the remaining $975,000 was for Ms Lane's pain and suffering.
Legal scholars said the settlement was unusual not just because of its size but because it is rare for companies to make third party payments, as they will to Columbia university, or to agree to a form of regulation, however ad hoc.