Budd was born in Delaware in 1870. He studied engineering in Philadelphia in 1888, and in 1899 he took his knowledge of pressed steel to the railroad industry. He worked with the Pullman Company on a contract for Pennsylvania Railroad, building the first all-steel car.
In 1912 he founded the Budd Company, which initially specialized in the manufacture of pressed-steel frames for automobiles. His company was soon supplying an all-steel sedan body to auto manufacturers such as General Motors, Studebaker, Willys, Oakland and Tatra. His first big supporters were the Dodge brothers, who purchased 70,000 bodies in 1916. However, Dodge placed the steel bodies onto conventional chassis frames. Budd envisioned pushing his technology even further ,and in 1924 he found another visionary in André Citroën. By 1934, they had developed the Citroën Traction Avant, the first unibody, pressed steel automobile. William Morris, founder of the Morris Motor Company in the United Kingdom, was also in tune with Budd's philosophy, and in 1926 he and Budd set up the Pressed Steel Company in Cowley, Oxford, to produce car bodies for Morris.
In order to hold all this steel together, Budd also pioneered the use of arc welding in automobile manufacturing.
During the Great Depression in the 1930s, Budd pioneered the fabrication of stainless steel and helped create the Pioneer Zephyr, a streamlined train for the Chicago, Burlington and Quincy Railroad. During World War II, Budd was also the original maker of the Bazooka projectile and the rifle grenade.