Constance was a younger daughter of Duke Leopold VI of Austria and his wife, the Byzantine princess Theodora Angelina, granddaughter of Emperor Alexios III Angelos.

In 1225 her elder sister Margaret married the 14-year-old Henry (VII), King-elect of Germany and eldest son of the Hohenstaufen emperor Frederick II.

Present at the wedding were King Wenceslaus I of Bohemia and Prince Béla IV of Hungary, the Archbishop of Salzburg as well as the bishops of Passau, Bamberg, Freising and Seckau.

Her husband, who had inherited both the Margraviate of Meissen and the March of Lusatia from his father, the late Margrave Theodoric I, participated in a Prussian Crusade of the Teutonic Order soon after their wedding.

He remained a loyal supporter of Emperor Frederick II, who betrothed his daughter Margaret of Sicily with Henry's and Constance's first-born son Albert.