Hans Hofmann was born in Weißenburg, Bavaria on March 21, 1880, the son of Theodor and Franziska Hofmann. When he was six he moved with his family to Munich. Here his father took a job with the government.

Starting at a young age, Hofmann gravitated towards science and mathematics. At age sixteen, he started work with the Bavarian government as assistant to the director of Public Works where he was able to increase his knowledge of mathematics. He went on to develop and patent such devices as the electromagnetic comptometer, a radar device for ships at sea, a sensitized light bulb, and a portable freezer unit for military use. Even with such great abilities in science and mathematics, Hofmann became interested in creative studies, beginning educational art training after the death of his father.
In 1932 he immigrated to the United States, where he resided until the end of his life.

Hofmann's art work is distinguished by a rigorous concern with pictorial structure, spatial illusion, and color relationships.

His completely abstract works date from the 1940s. Hofmann believed that abstract art was a way to get at the important reality. He famously stated that "the ability to simplify means to eliminate the unnecessary so that the necessary may speak".

Hofmann was renowned not only as an artist but as a teacher of art, both in his native Germany and later in the U.S. In Munich he founded an art school, where Louise Nevelson, Wolfgang Paalen, Worth Ryder[5] and Alfred Jensen, were among his students. He closed this school in 1932, the year he immigrated to the United States.
In America, he initially taught a summer session at the University of California, Berkeley in 1930, after which he returned to Munich. In 1931 he taught another summer session at the University of California, Berkeley and a semester at the Chouinard Art Institute in Los Angeles before again returning to Germany. After Hofmann relocated to New York City he began teaching in 1933 at the Art Students League of New York. Leaving the League in the mid-1930s Hofmann opened his own schools in New York and later in Provincetown, Massachusetts. Many famous or notable artists, especially some who could generally be classified as abstract expressionists, studied with Hofmann in New York and Provincetown.

In 1958, Hofmann closed his schools in order to devote himself exclusively to his own creative work. Hofmann is a painter and theorist of particular appeal to other artists. American painter Walter Darby Bannard  and British artist John Hoyland  both have been involved in curating retrospectives of Hofmann's work.

Also prominent as a writer on modern art, Hofmann authored an influential book (sometimes referred to and anthologized as an "essay"), Search for the Real, in which he discussed his push/pull spatial theories, his reverence for nature as a source for art, his conviction that art has spiritual value, and his philosophy of art in general. Hofmann is especially noteworthy as a theorist of the medium who argued that "each medium of expression has its own order of being," "color is a plastic means of creating intervals," and "any line placed on the canvas is already the fifth."