Ahmed Muse Salad, Abukar Osman Beyle and Shani Nurani Shiekh Abrar face the death penalty if convicted of murder, kidnapping and other charges.
The owners of the S/V Quest and two others were taken hostage for ransom as they sailed around the world.
They were killed as rescue negotiations with the US Navy broke down.
The three are accused of maintaining an armed guard over the Americans and intentionally shooting and killing them “without provocation before the hostages could be rescued by members of the military”.
Eleven other men have pleaded guilty to piracy in the case and have been sentenced to life in prison. They are expected to testify in federal court in Virginia against the three charged with murder in exchange for the possibility of reduced sentences.
Jury selection began on Tuesday in Norfolk, Virginia, home to the US Navy’s Atlantic fleet. The trial is expected to last five to six weeks.
The three accused Somalis followed the court proceedings with the help of two simultaneous interpreters.
About 100 people are on the list of potential witnesses, including US military personnel, FBI agents, forensic experts, relatives of the deceased and Somali nationals.
Jean and Scott Adam and their guests Bob Riggle and Phyllis Macay were the first US citizens killed in a wave of pirate attacks that plagued the Gulf of Aden and the Indian Ocean in recent years.