The union, which is part of the NewsGuild of New York, pledged to strike 24 hours a day last week if an agreement was not reached by Thursday.
It will be the first time New York Times workers have participated in a walkout since the late 1970s.
It comes amid a growing group of workers in the United States organized by workers at companies including Amazon, Starbucks and Apple to fight back against what they say are unfair labor practices.
Elsewhere in the media industry, reporters at the Pittsburgh Post-Gazette and Fort Worth Star-Telegram are currently working on open-ended strikes.
On November 4, more than 200 union journalists from 14 media outlets – including the Desert Sun and the Asbury Park Press – participated in a one-day strike.
In August, nearly 300 Reuters journalists in the United States, represented by New York's NewsGuild, staged a 24-hour strike as their union negotiated a new three-year contract with their company.