Unless otherwise provided in the articles or bylaws, a vacancy created by the resignation of an officer (or otherwise) is filled by approval of the board. Corp. Code §7213(b). This general principle is also described in Robert's Rules of Order:

The power to appoint or elect persons to any office or board carries with it the power to accept their resignations, and also the power to fill any vacancy occurring in it, unless the bylaws expressly provide otherwise. (Robert's Rules, 11th ed., p. 467.)

That means a majority of the remaining directors have the power to fill the vacancies. The president may participate in the process but the president does not have the power to be the sole determiner in the selection of replacement officers.