In a statement, the Israeli military said Prime Minister Benjamin Netanyahu had authorised the operation against Al-Atta, blaming him for recent rocket, drone and sniper attacks against Israel, and attempted infiltrations into the country.
Syria's state-run news agency says Israel has struck a residential building in Damascus housing a commander of the Palestinian Islamic Jihad group with two missiles, killing two people.
The Islamic Jihad confirmed Abu el-Atta, the commander, was killed.
The IDF spokesman said that the forces targeted al-Ata because he was "a ticking bomb" and was allegedly plotting "imminent" attacks on Israel. The house was known to be Abu el-Atta's home.
Two rockets targeted the home of a senior figure of the Palestinian group, Akram Al Ajouri, "killing his son Muadh and another person", SANA said.
The militant group said Abu el-Atta, 42, was undergoing "a heroic act" when he was assassinated.
Shortly after, Palestinian militants launched a salvo of rockets into Israel, setting off sirens as far as its port city of Ashdod, some 20 km (12.5 miles) away, witnesses said.
There were no immediate reports of injuries. A large crowd of people carried the bodies of Abu al-Atta and his wife through the streets of Gaza after the strike, calling for revenge. Police closed roads on the Gaza outskirts as a precaution.
Gaza's Hamas rulers are threatening to avenge the targeted killing of a top commander from the smaller Islamic Jihad group in the coastal strip.
Sirens sounded across Israel's southern towns and cities on Tuesday morning as incoming rockets descended from the Gaza Strip.
Israel had no further plans to resume its assassinations of militant leaders _ a practice that in the past has triggered heavy fighting. "There was no other choice", he said.
Since the 2014 war, Israel has mostly refrained from targeted assassinations of senior Gaza militants, but did so one time in May, Israeli airplanes killed a Hamas commander and financial broker in a vehicle traveling in Gaza City during a three-day exchange of fire.
The overnight attacks mark a significant escalation in the conflict between Israel and the Palestinian militant groups, which have fought each other in wars and cross-border violence for years.