A vacancy in the office of the Vice President of the United States is filled with a Presidential nomination that is confirmed by a majority vote from the House of Representatives and the Senate. This process applies whether the Vice President resigns or has to take over as President, leaving his former office vacant.
The 25th Amendment to the Constitution became law in 1967 after it was approved by Congress, ratified by the states and certified by the President. It outlined the process of filling a Vice Presidential vacancy, as well as a Presidential one. Until that time, the Constitution was unclear on the matter. Within a few years, the amendment proved helpful on more than one occasion. President Nixon took office in January of 1969 with Spiro Agnew as his Vice President. Agnew resigned in Nixon's second term of office on Oct. 10, 1973. President Nixon then nominated Gerald Ford to replace him, and Ford was confirmed by Congress. President Nixon resigned the Presidency on Aug. 8, 1974, and Gerald Ford took the oath of office the next day, again leaving the Vice President's office vacant. Ford nominated Nelson Rockefeller to fill the vacancy, and Congress then confirmed Rockefeller.