DiGirolamo was arrested last week at his parents' Brooklyn home. He has been charged with killing Giordano and trying to cover it up.
Giordano has been missing since June. Last weekend, authorities discovered skeletal remains believed to be Giordano's in a remote Staten Island pond.
Meidt said Friday that authorities believe the remains are Giordano's because pictures of her son were inside the suitcase.
He said investigators believe DiGirolamo killed Giordano with a blunt object in her Highstown apartment last June before sawing her body into pieces and stuffing it into a suitcase.
DiGirolamo was arraigned Friday in Mercer County. A judge ordered his bail to remain at $1 million.
DiGirolamo appeared via a television feed from the county jail in Hopewell. Bearded and wearing an orange jumpsuit, he kept his eyes to the ground during much of the hearing.
His lawyer, Jerome Ballarotto, said DiGirolamo planned to fight the charges.
"The state's case is extremely circumstantial," Ballarotto said. "It's based on statements made by individuals whose veracity and credibility have not been tested in any way whatsoever."
The remains were found with the help of John A. Russo Jr. of Staten Island, an alleged accomplice of DiGirolamo's who has been speaking with investigators. Russo is expected to soon face his own arraignment for evidence tampering.
According to prosecutors, Russo knew of the killing before the fact, helped DiGirolamo buy drain cleaner, reinforced garbage bags and a saw blade to use in the killing. Meidt told the judge that Russo also waited for DiGirolamo in Staten Island to help dispose the body on June 9.
Russo's lawyer could not be immediately be reached for comment.
Besides Russo, authorities also had testimony from friends who say DiGirolamo told them about the killing, said Meidt, who declined to name the friends.
Giordano was last seen alive on June 7. Two days later, her 11-month-old baby was found abandoned in the parking lot of Christiana Hospital in Newark, Del.
DiGirolamo has since admitted he left the child, even as he argues through his lawyer that he had nothing to do with Giordano's disappearance. He pleaded guilty in November to reckless endangerment and child abandonment. The child remains in foster care in Delaware.
DiGirolamo faces a term of 30 years to life in prison if convicted of the murder and evidence tampering charges against him.
Ballarotto said after the hearing that his client had four-hours notice last week that he was going to be arrested.
"Why sit in your parent's house, with your passport in a dresser drawer, with a four-hour head-start, if you're not an innocent man?"