Georg Buch was born in Wiesbaden on September 24, 1903. Even during his apprenticeship as a typesetter, he was involved in the youth organization of the Association of German Book Printers. In 1921, he joined the SPD, for which he was elected to the city council for the first time in 1933; at the same time, he became chairman of the Wiesbaden SPD. After the National Socialists seized power, he was temporarily taken into protective custody and interned in various concentration camps from 1941 to 1945.

After the Second World War, he played a key role in the political reconstruction of the city as managing director of the SPD Wiesbaden and later as a city councillor and head of the Department of Food and Economic Affairs. Between 1946 and 1950 and between 1954 and 1974, he was a member of the Hessian state parliament for the newly created state of Hesse. During these legislative periods, he was active at times as parliamentary group leader and from 1966 to 1974 as president of the state parliament. In 1954, he became Mayor of Wiesbaden and served as Lord Mayor from 1960 to 1968.

His services to the city and the state were recognized on 1 October 1968 when he was awarded an honorary citizenship. At this reception, Buch signed the city's Golden Book in his honor.