Finnegan Lee Elder and Gabriel Natale-Hjorth have been charged with killing newlywed Mario Cerciello Rega, 35, who was stabbed 11 times during the attack last July.
The Californians, who had been on holiday in Rome and were teenagers at the time, face a life sentence if convicted.
In Italy, the slaying aroused an outpouring of public sympathy for Cerciello, who had just returned from his honeymoon when he was killed. Huge crowds attended his funeral, which was broadcast live on television, where he was hailed as a hero.
“His murder cannot and must not go unpunished,” his wife, Maria Rosaria Esilio, said in a statement on the eve of the trial.
“My family has ended with Mario's death, because our unborn children and dreams were buried with him,” she said.
But the case has been marked by major blunders — especially the blindfolding of Natale-Hjorth during his police interrogation — and contradictory statements made by the key prosecution witness, Cerciello's
partner Andrea Varriale.
In the aftermath, Varriale said he and Cerciello had been attacked by men of North African descent. He also initially claimed he had been armed. Both officers were in fact unarmed and acted without backup, in violation of police procedure.
Amid the intense media focus in the case, comparisons have been made to the high-profile trial of Amanda Knox, a US student convicted and later acquitted of a 2007 murder in Italy.
Elder has admitted to stabbing Cerciello with a 7-inch (18 cm) serrated-edge combat knife he had stashed in his sweatshirt but told investigators he thought he and his friend were being set upon by drug dealers.
The young men and Varriale have given opposing versions of what happened during the 32-second attack in the early hours of the morning, which followed a drug deal gone wrong.
Hours earlier, the young men from the San Francisco Bay Area had gone looking for cocaine in the popular night-life area of Trastevere. Intermediary Sergio Brugiatelli introduced them to a dealer who sold them aspirin instead.
In retaliation, the teens stole Brugiatelli's bag, before demanding money and drugs to return it.
Cerciello and Varriale went in Brugiatelli's place to the designated exchange point in an upscale neighbourhood near the teenagers' hotel but the handover never took place.
Elder, now age 20, told police they were jumped from behind by the officers and believed they were thugs sent by Brugiatelli.
Varriale has said he and Cerciello, both in plain clothes and unarmed, told the young men they were police, but that Elder pulled out a knife and attacked Cerciello, while Natale-Hjorth wrestled with Varriale.
The teens then fled to their nearby hotel, where police later found the military knife hidden behind a ceiling panel.
Under Italian law, Natale-Hjorth, who was 18 years old last July, faces the same charge of “voluntary homicide” with a special circumstance of killing a police officer, even though he did not stab Cerciello.
Both young men are also charged with attempted extortion. They face a maximum penalty of life imprisonment in isolation.