The lost tomb of Caligula has been found, according to Italian police, after the arrest of a man trying to smuggle abroad a statue of the notorious Roman emperor recovered from the site.

After reportedly sleeping with his sisters, killing for pleasure and seeking to appoint his horse a consul during his rule from AD37 to 41, Caligula was described by contemporaries as insane.

With many of Caligula's monuments destroyed after he was killed by his Praetorian guard at 28, archaeologists are eager to excavate for his remains.

Officers from the archaeological squad of Italy's tax police had a break last week after arresting a man near Lake Nemi, south of Rome, as he loaded part of a 2.5 metre statue into a lorry. The emperor had a villa there, as well as a floating temple and a floating palace; their hulks were recovered in Mussolini's time but destroyed in the war.

The police said the statue was shod with a pair of the "caligae" military boots favoured by the emperor – real name Gaius Julius Caesar Augustus Germanicus; as a boy, Gaius accompanied his father on campaigns in Germany; the soldiers were amused he wore a miniature uniform, and gave him his nickname Caligula, or "little boot".

The statue is estimated to be worth €1m. Its rare Greek marble, throne and god's robes convinced the police it came from the emperor's tomb. Under questioning, the tomb raider led them to the site, where excavations will start today.