Büchel was born on 26 February 1922 in Gamprin as the son of mayor of GamprinWilhelm Büchel and Maria Wohlwend as one of eight children.[1][2] He attended secondary school in Freiburg im Breisgau. From 1945 to 1950 he studied law in Freiburg im Breisgau and Innsbruck. From 1950 to 1954 he worked in the Liechtenstein government office and as a lawyer in the Alfred Bühler law firm in Vaduz. He opened his own law firm in 1954, which he ran until 1988.[1]
From 1955 to 1966 and again from 1966 to 1970 he was the president of the Liechtenstein Bachelor of Laws administrative board.[1] From 1957 to 1982 Büchel was a member of the Landtag of Liechtenstein as a member of the Progressive Citizens' Party. During this time, he was a member of the finance, audit and state committees.[3] He was also a member of the Gamprin municipal council from 1963 to 1966.[1]