The news came a day after Caroline Kennedy, the initial frontrunner to take the spot left open by now Secretary of State Hillary Clinton, withdrew her name from consideration for the position, citing personal reasons.
Paterson is expected to make the announcement at noon Friday in Albany. An aide to Rep. Gillibrand confirmed to the New York Times that she had accepted the position.
Gillibrand, a 42-year-old second-term lawmakerfrom upstate New York, would remain in the Senate seat until 2010, when a special election will be held to choose a new senator.
While Gillibrand did not have the name recognition of Kennedy or state Attorney General Andrew Cuomo, another frontrunner, she had been rumored to be one of the contenders in Paterson's search.
The Times reported that Paterson has hoped to choose a woman to fill Clinton's vacant post.
"Gender plus geography equals Gillibrand," Doug Muzzio, a political science professor at Baruch College told the AP. He said that Gillibrand's upstate base would help Paterson's own 2010 run for re-election. Paterson, the former lieutenant governor of New York, was appointed to the governor's post after former New York Gov. Eliot Spitzer resigned amid a prostitution scandal last year.
An official in the Housing and Urban Development Department during former President Bill Clinton's administration, Gillibrand had never held public office before winning her current House seat in 2006 against four-term Republican, Rep. John Sweeney.
The race turned particularly negative toward the end, with Sweeney accusing Gillibrand of being behind a leaked report that revealed police had been called to his house in response to a domestic disturbance. Eventually, Mr. Sweeney admitted that the police had actually been called to his home and Gillibrand went on to win the race with 53 percent of the vote.
But while Gillibrand has won wide support in her eastern New York district, more senior Democratic politicians, including fellow New York Rep. Carolyn McCarthy, have criticized her support of more conservative issues such as gun ownership rights.
McCarthy, an ardent gun control activist, told the New York Times on Thursday that she would run against Gillibrand in 2010 if she were offered the open Senate seat.
Gillibrand is considered one of the fiscally conservative Blue Dog Democrats and voted against the $700 billion Wall Street bailout bill last year.
Kennedy, the daughter of slain President John F. Kennedy, made an early bid for the Senate spot and received a blizzard of media attention for her efforts. However, she appeared to struggle with the adjustment to life in the public eye and was also concerned with the continuing health problems of her uncle, Sen. Ted Kennedy, ultimately leading her to withdraw from contention, according to media reports.