Galileo died on 8th January 1642 after suffering with a fever and heart palpitations. He was aged 77 at the time of his death.
From 1634 he had been under house arrest at his villa near Florence after being put on trial in Rome after his writings were seen to mock the Pope. He was put under house arrest because he wanted the least harshist punishment possible. It was there he remained until his death 8 years later.
By 1638 Galileo went completely blind and was suffering from insomnia and a painful hernia.
After Galileo's death The Grand Duke of Tuscany had wished to bury him in the main part of the Basilica of Santa Croce (a church in Florence) and erect a mausoleum in his honour however Pope Urban VIII protested because Galileo was condemned by the Catholic Church for vehement suspicion of heresy.
So, although he was still buried in the Basilica, he was then to be buried in a small room at the southern transept of the building. However in 1737 a monument was erected in the main body of the Basilica and Galileo was reburied along with it.
To this day tourists can visit the Museo Galileo in Florence and see one of Galileo's fingers which was removed during his reburial.