Marissa Shorenstein, a spokeswoman for Paterson, said the governor's office delivered paperwork in Washington on Sunday formalizing Gillibrand's appointment to the Senate.
Gillibrand, a second-term congresswoman who worked on the former first lady's 2000 Senate campaign, said Clinton "has always been a mentor of mine and someone I've always admired."
Paterson appointed Gillibrand after the presumed front-runner, Caroline Kennedy, withdrew from contention over personal reasons.
Paterson said at a news conference that, "Caroline Kennedy ... had gotten no indication that she wouldn't be selected."
Appearing earlier on "Fox News Sunday," Schumer said he was happy with Paterson's choice but added that Gillibrand's rural district was "more like Montana than New York City."
Gillibrand's voting record has earned her a 100 percent rating with the National Rifle Association, and her pro-gun stance is at odds with the views of many politicians in New York City and other downstate areas.
Gillibrand said she was grew up a family of hunters, and that she had "always believed in protecting hunters' rights. ... It's a core value for our region and for our state."
But she acknowledged there was "concern in our city communities about gun violence."
Shorenstein said Gillibrand likely would be sworn in Tuesday.