Andreas was the son of Thomas Palaiologos, Despot of Morea, and Catherine Zaccaria, the daughter of Centurione II Zaccaria the last Prince of Achaea. After his uncle Constantine XI Palaiologos, the last Emperor of Constantinople died defending the capital of the Byzantine Empire on May 29, 1453, Andreas' family continued to live in Morea as vassals of the Turkish Sultan Mehmet II. But constant bickering between Thomas Palaiologos and his brother Demetrios led to the Sultan invading the Morea in 1460; Andreas and his father escaped to Corfu. His father Thomas then left the rest of the family to go to Rome, where he made a ceremonial entrance as Byzantine Emperor 7 March 1461. Andreas' mother died in August 1462, but he and his younger brother Manuel did not rejoin his father until a few days before the man died in 1465. After his father's death, Andreas stayed in the Papal States by consent of the Pope. He lived in Rome, styling himself Imperator Constantinopolitanus ("Emperor of Constantinople"). Andreas was considered by his contemporaries, most prominently the Cardinal Bessarion the rightful heir to the Roman (Byzantine) throne who, curiously, lived in Rome years after the end of the Eastern Roman Empire.
Despite the great expectations Papal officials had for Andreas, his behavior was not imperial. In 1480 he married Caterina, a woman Runciman describes as "a lady from the streets of Rome"; and he constantly lived beyond his means. During his lifetime, Andreas was believed to have wasted enormous sums of money given to him by the Pope; however, modern historians now believe that the money received from the Pope was only enough for a meager style of life.
Desperate for money, Andreas sold the rights to the Byzantine crown which he possessed since the death of his father. Charles VIII of France purchased the rights of succession from Andreas during 1494 and died on April 7, 1498. The following Kings of France continued the claim and used the Imperial titles and honors: Louis XII, Francis I, Henry II and Francis II. Not until Charles IX in 1566 did the imperial claim come to an eventual end through the rules of extinctive prescription as a direct result of desuetude or lack of use. Charles IX wrote that the imperial Byzantine title "is not more eminent than that of king, which sounds better and sweeter."
Andreas died a pauper during 1502, in spite of having sold his titles and royal and imperial rights again to Ferdinand II of Aragon and Isabella I of Castile. However, Runciman doubts he ever received any money due, for his widow had to beg the Pope for 104 ducats to pay the costs of his funeral.
Andreas visited his sister Sophia Palaiologina, wife of Ivan III of Russia, in Moscow during 1480 and 1491.
While most scholars believe Andreas left no descendants, Donald M. Nicol's The Immortal Emperor recognises Constantine Palaiologos who served in the Papal Guard, and a woman Maria who married the Russian noble Vasily Mikhailovich as possible son and daughter of Andreas.
An illegitimate daughter of Constantine Palaiologos is present in some Italian sources; she is identified as Domitia or Dominique, the concubine of Evandro Conti (a Roman nobleman descendant of the family of Pope Innocent III) and mother of his illegitimate sons: the children of this couple, Mars (Marzio) and John Caesar (Giovanni Cesare) Conti, did not claim their rights to the throne of Constantinople.
Russian sources tell of a great scandal in Moscow regarding Maria, the niece of Sophia, Andreas's sister. The Grand Duchess arranged the marriage of her niece with Prince Vasily Mikhailovich of Vereya-Belozersk (dynasty of princes of Mozhaysk). Vasily was the son of Prince Mikhail Andreevich of Mozhaysk (Михаил Андреевич Можайский), who was the grandson of Grand Duke Dmitry Donskoy and cousin of Grand Duke Ivan III. During 1483 Sophia gave to her niece a necklace from the dowry of Ivan III's first wife Maria of Tver, mother of her stepson Ivan the Young, the heir. When Ivan III wanted to present the same necklace to Ivan the Young's wife Elena of Moldavia he found that the jewel was missing. Because of this scandal, Maria and her husband Vasiliy escaped to Lithuania, and Mikhail Andreevich of Mozhaysk lost the Principality of Vereya. Only during 1493 did Sophia persuade her husband to forgive Maria and Vasiliy.