"I believe I have found the best candidate to become the next U.S. senator from New York," Paterson said during a news conference in Albany, N.Y.
Gillibrand was appointed to finish the unexpired term of Clinton, who was sworn in Wednesday as U.S. secretary of state, CNN reported.
"I aspire to follow in her footsteps, knowing her shoes I can only hope to fill," Gillibrand said of Clinton.
Gillibrand represents New York's conservative 20th Congressional District and is a member of the fiscally conservative Blue Dog Coalition.
Notable deaths of 2014 [PHOTOS]