Herbst was born in Rakvere, Russian Empire (now Estonia), the son of Wacław Chrobot, a banker and artillery lieutenant, and Maria of Nowohoński (from landed nobility).

His lecturers included Henryk Mościcki, Wacław Tokarz and Oskar Halecki, under whose supervision he defended his PhD in 1931 (based on the work War of Livonia, 1600–1602).

He also worked at the Ministry of Religious Denominations and Public Enlightenment, where he was an official in the Department of Religions (1935–1937) and a scientific adviser to ministers (1937–1939).

After the outbreak of World War II, he initially worked at the Archive of the Nieśwież Ordnance, then at the antique shop of Czesław Garliński, the National Library and the University Library in Warsaw; together with Piotr Biegański, Stanisław Lorentz and Jan Zachwatowicz, where he saved works of art during the Warsaw Uprising.

In addition to the University of Warsaw, Herbst was associated with the Institute of History at the Polish Academy of Sciences from 1953 to 1961 and was head of the Historical Atlas Unit, the Dzerzhinsky Political-Military Academy in Warsaw from 1957 to 1968 and was head of the Department of Military History and War Art, Mazovian Center for Scientific Research in Warsaw (chairman of the Scientific Council from 1967) and the Jewish Historical Institute in Poland (from 1969 chairman of the Scientific Council).

He took part in the International Historical Congresses in Vienna (1965) and Moscow (1970), sat on the Civic Committee for the Reconstruction of the Royal Castle in Warsaw (from 1971) and in the Capital City Council from 1958 to 1962.

Among the prizes and distinctions that Herbst received include the 1st degree award of the Minister of National Defense (1968, for research on the Kościuszko Uprising), the Knight's Cross (1947)[3] and Officer's Cross (1966) of the Order of Polonia Restituta, Order of the Banner of Work 2nd class (1966), and title of Teacher of Merit of the Polish People's Republic (1969).

A street commemorating Herbst is located in the Ursynów district of Warsaw, between Al. National Education Commission and Capt.