The agreement is the latest success in an Italian campaign to recover artifacts that survived for centuries only to be dug up by looters, smuggled out of the country and sold to prestigious museums across the world.
Director Timothy Rub stressed that the Cleveland museum had not knowingly acquired or received looted items. He said they were bought or donated to the museum in the 1970s and 1980s.
The treasures to be returned from Cleveland are mostly a sampling of art produced by the Etruscans and by Greek-influenced cultures that dominated central and southern Italy before the rise of Rome.
The objects are "of great historical, artistic and archaeological interest," Italian Culture Minister Sandro Bondi said.
Among them are a pair of Etruscan silver bracelets from the 6th century B.C. and a bronze statue of a horned warrior, dated to the 9th-8th century B.C., which experts said is one of the finest remaining from a civilization that populated the island of Sardinia.
Most of the artifacts are elaborate and richly decorated pottery pieces from 5th to 4th century B.C. southern Italy.
They include vessels shaped as a donkey head, a pig and a duck as well as a 1-meter-tall (3-foot-tall) vase attributed to the so-called painter of Darius - an artist named after one of his works which depicts the ancient Persian king.
The odd object in the group is a 14th century gold-plated processional cross stolen in the 1960s from a church near Siena, in Tuscany.
The artifacts were shown to have been looted mainly because photos and documents related to them turned up in raids conducted in the 1990s on the Swiss warehouses of antiquities dealers accused of controlling the flow of illegal art exports from Italy. The raids sparked what has turned into a worldwide hunt for Italy's lost treasures.
The deal signed at the Culture Ministry came after nearly two years of negotiations that began when the museum contacted the Italians to check if Rome was seeking to recover any of its antiquities.
"When putting together a collection it is important that any museum acquire works ethically," Rub said.
Bondi and Rub said the two sides had established a joint commission to determine within six months the provenance of two more contested pieces: a statue depicting Nike, the winged victory deity, and a bronze of the Greek god Apollo.