His parents were Boček II of Poděbrady and Anna Elisabeth of Leipa (Czech: Anna Eliška z Lipé), a daughter of Henry of Leipa (Czech: Jindřich z Lipé).
Boček then inherited the Moravian estates jointly with his younger brother Victor.
Victor also inherited the Bohemian dominions Litice Castle and Náchod and the Lordship of Hummel, while the youngest brother Hynek Boček received the family seat at Poděbrady.
In 1417, Boček III successfully besieged Pyšolec Castle; a year later he acquired the Lordship of Vranová Lhota.
After the start of the Hussite Wars, Boček III participated in a meeting at Brno, where the nobles were forced to reject the Four Articles of Prague and to obey King Sigismund of Bohemia.