After receiving his B.A. from Stanford University in 1934, Packard worked for the General Electric Company in Schenectady, N.Y. In 1938 he returned to Stanford, where he earned the degree of electrical engineer, and in 1939 he and William R. Hewlett established their firm in Packard's garage with capital of $538. The company, in which Packard proved to be an expert administrator and Hewlett provided many technical innovations, grew into the world's largest producer of electronic testing and measurement devices. It also became a major producer of personal computers and laser and inkjet printers. Packard served as Hewlett-Packard's president from 1947 to 1964, chief executive officer from 1964 to 1968, and chairman of the board from 1964 to 1968 and from 1972 to 1993.

In 1968 President Richard M. Nixon appointed Packard deputy to Secretary of Defense Melvin Laird. Packard served until 1971, when he resigned and returned to Hewlett-Packard the next year as chairman of the board. In the 1970s and '80s Packard was a prominent adviser to the White House on defense procurement and management.