In text messages to journalists and on Hamas' TV, Hamas identified the two attackers as Mohammed Herbawi and Shadi Zghayer.
One woman was killed and 11 people were wounded in Monday's attack in the southern Israeli town of Dimona.
The Popular Front for the Liberation of Palestine later declared that its men were behind the attack, along with Hamas.
Hamas' announcement ended a day of contradictory information and speculations regarding the identity of the attackers and the place they left from towards Dimona.
At first, defense officials believed that the bombers took advantage of the breached fence at the Gaza-Egypt border to infiltrate Israel.
Hours after the attack, a Hamas source told the Reuters news agency that the organization's members were responsible for the attack, but this was denied by group officials.
Security forces continued their investigation into the attack based on intelligence information, while examining the attackers' identity. The explosive belts they were carrying were also examined, as well as the route they took on their way to Dimona.
"We are doing everything we can to solve the terror problem coming out of Hebron and the Qassams coming out of Gaza," the defense minister told IDF cadets at the southern army base of Shizafon.
Hamas' announcement also clarified the bombers' identity. Several organizations in Gaza claimed that their men had carried out the attack, and even presented videos showing the alleged Dimona attackers.
President Shimon Peres told Ynet on Tuesday that "Hamas is making the chance of one state for the Palestinians impossible."
The president spoke while visiting people injured in the Dimona attack at the Soroka Medical Center in Beersheba.
Aviram Zino contributed to this report