The marriage of their parents, Ferdinand II, Archduke of Austria and Philippine Welser, was morganatic.

This meant that the brothers were not considered members of the Habsburg dynasty and could not use their father's title, Archduke of Austria, bearing instead that of Margrave of Burgau.

In March 1574, Andrew travelled to Rome, where Pope Gregory XIII made him a cardinal, with Santa Maria Nuova as his titular church.

In 1598 and 1599, he briefly served as acting Governor General of the Habsburg Netherlands while Archduke Albert VII travelled to Spain to marry Infanta Isabella Clara Eugenia.

His marble funeral monument in the church was completed by the sculptors Gillis van den Vliete and Nicolas Mostaert around 1600 and includes a portrait of Andrew kneeling in prayer.