The statement by Iran's Revolutionary Guards on Saturday also accuses the "criminal government" of the United States of supporting the attack, which Iran blames on Israel.
"This terrorist attack was designed and implemented by the Zionist regime (Israel) and supported by the criminal government of America," the IRNA news agency quoted the statement as saying.
The statement by IRGC which was televised on the country's state media, came, three days after Haniyeh was killed at his accommodation in northern Tehran following his attendance at the inaugural ceremony of Iran's new president Masoud Pezeshkian.
As per the statement, a rocket with a seven-kilogram warhead was used to target the residence of Haniyeh state media IRNA reported.
It said the attack caused heavy devastation.
The IRGC statement emphasised that it would "avenge blood of Haniyeh", adding that "the terrorist and adventurist Zionist regime would definitely receive severe punishment and a decisive response at appropriate time and in proper place."
The Hamas leader and his bodyguard were killed in an Iranian government guest house in Tehran in the early hours of July 31. Haniyeh had gone to the Iranian capital to attend the inauguration of Iran's newly elected president, Masoud Pezeshkian.
Iran and Hamas have accused Israel of the killing. Israel, which is at war with Hamas in the Gaza Strip, has neither acknowledged nor denied killing Haniyeh.
Iran's Supreme Leader Ayatollah Ali Khamenei led a public funeral ceremony for Haniyeh in Tehran on Thursday, before the coffin was transported to Doha, and threatened "harsh punishment" for Haniyeh's killing.
Earlier on Wednesday, he also ordered Iran to strike Israel directly, in retaliation for the killing of Hamas leader. Khamenei gave the order at an emergency meeting of Iran's Supreme National Security Council.
Hanieyh's killing came hours after top Hezbollah commander Fuad Shukr was killed in an Israeli air attack on the southern suburbs of Lebanon's capital, Beirut, on July 30
Iranian news agency IRNA quoted Hezbollah's Al-Manar TV as saying on Saturday that fighters of the Tehran-backed Lebanon group had targeted a building where Israeli soldiers gathered earlier in the day.
Air raid sirens went off in 15 Israeli settlements, the Al Mayadeen TV channel reported.
Hezbollah said it launched a barrage of Katyusha rockets towards the Beit Hillel settlement in northern Israel, claiming the attack was in response to Israel's targeting of civilians in Lebanon, according to a report in Al Jazeera.
Videos showed Israel's Iron Dome defence system being activated over the area.
Meanwhile, during a meeting in Doha, Iran's Vice President Mohammad Reza Aref and Qatar's Emir Sheikh Tamim bin Hamad bin Khalifa Al Thcalled for an immediate ceasefire in the Gaza Strip.
They also discussed Iran's call for an extraordinary meeting of the Organization of Islamic Cooperation (OIC) member states over the assassination of the Hamas leader, IRNA reported.