Reichsfürst
Anton Egon was born in Munich, where his father Count Herman Egon of Fürstenberg-Heiligenberg (1627–1674) served as privy councillor at the court of the Wittelsbach elector Ferdinand Maria of Bavaria. He was the eldest son from his father's marriage with his cousin, Countess Maria Franziska of Fürstenberg-Stühlingen (1638–1680). In 1664 Emperor Leopold I elevated the Fürstenberg-Heiligenberg branch to the rank of Princes of the Holy Roman Empire. Upon his father's death in 1674, Anton Egon succeeded as head of the line.