Sullivan, who most recently was former U.S. Secretary of State Hillary Clinton's deputy chief of staff, is a graduate of Yale Law School and a Rhodes Scholar.
He succeeds Tony Blinken, who was appointed by President Barack Obama to be his principal deputy national security adviser, the statement said.
"Jake is the ideal person to serve as my national security adviser," Biden said. "He has been a part of some of the biggest foreign policy challenges our nation has faced and he's always handled himself with incredible skill."
His formal title will be deputy assistant to the president and national security adviser to the vice president.