He was the son of John Theodore Callimachi, Prince of Moldavia, and Ralitsa Chrysoskoleos.

Alexander had three siblings: Gregory Callimachi (1735–1769), Prince of Moldavia; sister, Sevastitsa (born 1736), who married Michael Drakos Soutzos, Prince of Moldavia; and sister, Maria (1740–1831).

His uncle Gavriil Callimachi (1689–1786) was a monk at Putna Monastery before he founded the St. George Cathedral in Iași.

Their first son, the hospodar Scarlat Callimachi, was Prince of Moldavia at three different times, while Scarlat's son Alexandros was conferred the Ottoman title of Bala in June 1861, the first Christian to be so honored.

Callimachi died in Bolu in 1821,[1] the same year that Phanariote rule ended with the outbreak of the Greek War of Independence against the Ottoman Empire.