Rome's Colosseum will soon look a little more like it did in the bad old days two millennia ago, when it first hosted gladiator fights, mock naval battles and public executions carried out by wild animals.

The $35 million project—the first full cleaning in the Colosseum's history—aims to return it to its former splendor, while also strengthening the overall structure. Earthquakes, the pillaging of pieces of its outer frame, heavy car traffic and Rome's nearby subway have damaged key parts. The scrubdown should also reveal...