One of the most important pieces of Greek art in existence, a large painted terracotta urn known as the “Euphronios Krater”, recently left New York’s Metropolitan Museum for ever. It joins 68 other works, mainly Greek and Etruscan, all purloined from Italy during the past 30 years, all now safely “home”.

They can be seen in a triumphant show in the grandest site in Rome – the Quirinale palace – once the home of popes and now of presidents. In spite of their astonishing quality, the antiquities are almost overshadowed by the heavy baroque setting. Pope Alessandro VII’s gallery, running along three sides of the internal courtyard on the piano nobile, is a riot of gilt and ormolu mirrors and clocks, with tapestries, chandeliers and walls decorated either with frescoes by Pietro di Cortona or slabs of marble.

The star of Nostoi: Capolavori Ritrovati ( nostoi means “homecomings” in Greek) is undoubtedly the red-figure Euphronios vase, dating from the 6th century BC and named after its maker.

It is large (47cm high) and handsome and the only piece to have come down to us intact. The inventor of the red-figure technique is known to have made and painted 27 of them between 520BC and 470BC.

The painting on the front shows the dying Sarpedon, son of Zeus and the moon-priestess Laodameia, spouting blood from wounds inflicted during the Trojan war. He is tenderly carried by two winged and armoured figures, Hypnos and Thanatos (personifications of sleep and death), watched over by the messenger Hermes.

Euphronios uses stronger or more diluted colour to give volume, and this, along with his skilled foreshortening and accurate knowledge of anatomy, imbues the scene with a high sense of drama.

Returning the Euphronios vase to its rightful owners must have been a wrench for the Met ropolitan. It had been in the museum since 1972, having been stolen from the Etruscan necropolis at Cerveteri, just north of Rome, probably in 1971. A black-market dealer bought it from the tombaroli (tomb robbers) and sold it to the museum for $1m.

The J Paul Getty Museum in Malibu, the Boston Fine Arts Museum, the Princeton Museum and Jerome Eisenberg’s Royal Athena galleries have joined the Metropolitan in returning smuggled works to Italy.

There was also a last-minute arrival, a week before the show opened, from a private dealer in Switzerland with a guilty conscience: a bronze from the 2nd-century BC. Temporarily in Italy is a handsome kore (draped female figure) from the 6th-century BC, lent by Greece in gratitude for the energetic investigations carried out by the Italians. It will return to the Archaeological Museum in Athens when the show ends.

All the works here were stolen from archaeological sites scattered around Italy between 1972 and 2000. Many were obviously lost before that, but 1972 was taken as a convenient starting date. It was the year the Unesco Convention, which aims to prevent the smuggling of artworks, came into force. All have been returned against promises by the arts minister, Francesco Rutelli, of generous long-term loans, including loans of the contested pieces.

Negotiations opened in February 2006, when the previous arts minister, Rocco Buttiglione, convinced the Metropolitan’s director, Philippe De Montebello, to collaborate with Italian authorities. The carabinieri per la tutela del patrimonio culturale had dug up sufficient evidence of wrongdoing.

Where the Metropolitan has led, the J. Paul Getty Museum in Malibu has followed, in the wake of a lengthy trial. Legal proceedings in Rome last year involved (among others) Marion True, curator of antiquities at the Getty Museum between 1986 and 2005. Michael Brand, who took over as director there in December 2005, has returned no fewer than 40 works to Italy, all of which are on show here.

One of the largest and most famous statues is the 5th-century BC “Morgantina Venus” (so-called after the site in central Sicily where it was found). The two-metre statue has been in the Malibu museum since 1988 and will return to Italy only in 2010. Part of the reason for the delay is its starring role in a series of exhibitions already programmed, but there are also questions of ownership still to be resolved with the independent region of Sicily.

Perhaps the most dramatic restitution here is another two-metre figure: that of the elegantly veiled and coiffed Vibia Sabina, the wife who failed to provide the emperor Augustus with an heir. It has been returned by the Boston Fine Arts Museum.

There are numerous vases, serving different purposes, whose painted mythological scenes are always lively and often amusing. One is the 4th-century BC lekythos (funerary oil jug), stolen from Paestum and returned by the Getty. It shows the group of nymphs who were to offer immortality to Hercules. They are busy preening themselves in mirrors and feeding the tame-looking dragon that guards the tree with the golden apples.

The most unusual object, again from the Getty Museum, is a 4th-century BC sculptural group showing two griffins with upraised wings in the act of killing a terrified doe, their fangs embedded in its flanks. The residue of the original colours – blues, ochres and the red of running blood – make the work even more dramatic, and slightly disagreeable. Slightly flattened areas at the top of the wings indicate that the piece could have served as a table support.

Nostoi: Capolavori Ritrovati is certainly a coup for Italy, even though the final home of these magnificent pieces seems uncertain – apart from the Euphronios vase, which will go to the Villa Giulia museum in Rome. American museums that have been generous in making amends will have their reward in the form of loans.

The best news is a determination to share and make more visible and thief-proof the art of antiquity in general. Ultimately this art belongs to all of us.

The exhibition runs until March 30 at Palazzo Quirinale, Rome. www.quirinale.it/palazzo/arte-cultura