Biden took the oath of office from Supreme Court Justice Sonia Sotamayor during a private ceremony at the Naval Observatory, the vice presidential residence. About 120 friends and family witnessed the ceremony, Xinhua reported.
Biden's office said the vice president personally selected Sotomayor, who was the first Hispanic and fourth female judge to administer an oath of office for presidents and vice presidents.
The Bible used in the ceremony has been in the Biden family since 1893. Biden used it each time he was sworn in as a senator and when he first became vice president. His son Beau also used the Bible when he was sworn in as Delaware's attorney general.
President Barack Obama will also be officially sworn in at a low-key ceremony later Sunday morning, as required by the constitution.
Obama and Biden will be sworn in again at a public ceremony Monday, as dictated by tradition when Jan 20 falls on a Sunday. Obama will also deliver his inaugural address at the public ceremony.
An estimated 800,000 people are expected to attend Monday's inauguration and parade.
