Born in Imst, Tyrol, Gorbach served in the Austro-Hungarian Army at the Italian Front in World War I, was severely wounded in the 1917 Battle of Caporetto and lost a leg.

In 1937 he was appointed a minister (Landesrat) in the Styrian state government, However, upon the Austrian Anschluss to Nazi Germany in March 1938, Gorbach was dismissed and held as a political prisoner at Dachau concentration camp from 1938 to 1942, and again at Flossenburg from 1944 until the end of World War II.

After the war, Gorbach joined the newly established Austrian People's Party, and upon the 1945 legislative election became third president of the National Council parliament, an office he held until 1953 and again from 1956 to 1961.

Chancellor Gorbach led his party into the 1962 election with an anti-Socialist campaign, only to continue the grand coalition with the SPÖ under Vice-Chancellor Bruno Pittermann afterwards.

After three years as chancellor, conciliatory Gorbach had to vacate his position in favour of the less pragmatic ÖVP "reformers" around his successor Josef Klaus.