Q: When was the Roman empire sold, and who bought it?
A: On March 28th, 193 AD, the Roman empire was auctioned off by the Praetorian guards to the wealthy senator Didius Julianus for the price of 6250 drachmas per soldier.
This infamous offer, the most insolent excess of military licence, diffused an universal grief, shame, and indignation throughout the city. It reached at length the ears of Didius Julianus, a wealthy senator, who, regardless of the public calamities, was indulging himself in the luxury of the table. His wife and his daughter, his freedmen and his parasites, easily convinced him that he deserved the throne, and earnestly conjured him to embrace so fortunate an opportunity. The vain old man hastened to the Praetorian camp, where Suplicianus was still in treaty with the guards, and began to bid against him from the foot of the rampart.
A magnificent feast was prepared by his order, and he amused himself until a very late hour, with dice, and the performances of Pylades, a celebrated dancer. Yet it was observed that after the crowd of flatterers dispersed, and left him to darkness, solitude, and terrible reflection, he passed a sleepless night; revolving most probably in his mind his own rash folly, the fate of his virtuous predecessor, and the doubtful and dangerous tenure of an empire, which had not been acquired by merit, but purchased by money.
After the armies of Britain, Syria and Pannonia declared against Julian, a civil war began. The Praetorian guards eventually deserted Didius Julianus, and he was condemned and executed by the Roman Senate on June 2nd of the same year.
Source: Edward Gibbon, "The Decline and Fall of the Roman Empire", chapter V, volume I, first published in 1776.