The interior ministry said in a statement that it has shared its findings with Italy, which was helping investigate the abduction and murder of the Cambridge University graduate whose mutilated body was found in Cairo in January.
The ministry also released photographs of Regeni's passport, university identification cards and a wallet.
The manner of Regeni's abduction and killing provoked accusations in Italy of Egyptian police involvement, something Cairo had strongly denied.
Regeni, 28, had been researching labour movements in Egypt, a sensitive topic, and had written articles critical of the government under a pen name.
The incident threatened relations between Egypt and Italy, a strong supporter of President Abdel Fattah al-Sisi whose security services have been accused of abusing dissidents.
The ministry had announced earlier on Thursday that police had killed four members of a criminal gang that had kidnapped and robbed foreigners in Cairo in a shootout, without mentioning Regeni.
A later statement said they found the men, who were posing as police, inside a van and exchanged gunfire with them, killing them all.
"When they saw the police they fired at them. The police returned fire, resulting in their deaths," the interior ministry said.
Police then tracked down Regeni's belongings at the home of one of the gang members' sister.
"Italian security has been has been notified about the results," the statement said.
After Regeni's body was found, activists in Egypt and the Italian press initially pointed a finger at the Egyptian security services, which deny allegations by rights groups that they abduct and abuse dissidents.
Regeni had gone missing on the evening of January 25th, the anniversary of the 2011 uprising that overthrew veteran strongman Hosni Mubarak.
Police were out in force that day to prevent protests, and Regeni was last heard from as he walked to a metro station to meet a friend.
The interior ministry had said they believed criminals were behind Regeni's abduction and his brutal killing.
His body was found a week later at the side of a road on Cairo's outskirts, bearing the signs of brutal torture.
In an interview with an Italian newspaper this month, Sisi promised to "do everything" to find Regeni's killers.
"I promise you that we will do everything to shed light (on the case) and we will get to the truth," he told La Repubblica newspaper.
The statement on Thursday said an unidentified corpse with a gunshot wound was found in the gang's van, along with an assault rifle, an electric prod and fake police identification.
The gang had been responsible for at least nine robberies, including one involving another Italian, according to the ministry.
Their investigation led them to the apartment of one of the slain suspects' sister, where they found a leather bag that contained Regeni's passport wallet, the statement added.
The suspect's wife was also arrested at the apartment and said the bag belonged to her husband.