Anna was the eldest daughter of the elector Frederick I of Saxony (1370–1428) from his marriage to Catherine (1395–1442), daughter of Duke Henry I "the Mild" of Brunswick-Lüneburg.
Anna, with a dowry of 19,000 Rhenish gold florins, married on 8 September 1433 in Kassel Landgrave Louis I of Hesse.
Their engagement had been announced on the occasion of the Inheritance Treaty between the two houses in 1431 in Rotenburg an der Fulda.
Through this marriage, Louis increased his territory considerably.
He received the Saxon properties of Eschwege and Sontra from Anna's brother Frederick II of Saxony.