[Lucius Cornelius Sulla]

The President makes a nomination to be confirmed by the Senate.

For the benefit of those who have been mistaking things in the process of filling a vacancy in the Vice Presidency: According to the 25th Amendment to the Constitution:

Section 2.
Whenever there is a vacancy in the office of the Vice President, the President shall nominate a Vice President who shall take office upon confirmation by a majority vote of both Houses of Congress.

[AmericanInTokyo]

And that is exactly what Gerald Ford did, and Nelson Rockefeller emerged from behind the curtain to the horror of millions of conservative Republicans. I remember that moment.