Police say the boys were a two-year-old and a four-year-old.
They disappeared on Monday night when waves of water crashed into an SUV while they were being driven by their mother in the city's Staten Island borough.
The tragic news came as the death toll from Sandy continued to rise as swathes of the US East Coast battle to recover after the massive storm.
More than 80 people are now known to have died in the US, and others remain missing.
About 4.5 million people in 12 states are still without power, and chronic fuel shortages persist.
The National Guard is to deliver a million meals and bottled water to New Yorkers affected by the storm.
Meanwhile, Bruce Springsteen and Jon Bon Jovi, both from hard-hit New Jersey, will perform at a benefit concert for Superstorm Sandy victims.
Billy Joel of New York's Long Island, also badly damaged by the storm, is also scheduled to appear at the concert later today.
In New York, people returned to work as the commuter and subway trains began working again. The three major airports resumed at least limited service, and the New York Stock Exchange reopened.