Born in Berlin, Baumgart was promoted D. ph in 1956 in historical thinking at the Free University of Berlin with a work supervised by Carl Hinrichs on Zinzendorf.
He was Hinrichs' research assistant at the Friedrich-Meinecke-Institut [de] and habilitated in 1964 on the former Braunschweig-wolfenbüttelsche University of Helmstedt.
From 1967 until his retirement, Baumgart taught as full professor of modern history at the University of Würzburg.
About the Soldier King Baumgart wrote a biography in the anthology about Prussia's ruler.
Baumgart is a member of the executive committee of the Preußische Historische Kommission [de] sowie der Historische Kommission für Schlesien [de][2] Monographs Editions