Badreddine, 55, was one of the highest ranking officials in the group, and was believed by the U.S. government to be responsible for Hezbollah's military operations in Syria, where it is fighting alongside Syrian President Bashar al-Assad.
The killing of Badreddine, a brother-in-law of late Hezbollah military commander Imad Moughniyah, is the latest big loss sustained by Hezbollah and Iran in Syria despite Russian military intervention in support of Assad and his allies.
At least four prominent figures in Hezbollah have been killed since January 2015. A number of high-ranking Iranian officers have also been killed, either fighting Syrian insurgents or in Israeli attacks.
Hezbollah said Badreddine had been killed in a big explosion targeting one of its bases near Damascus airport, and an investigation was underway into whether it was caused by an air strike, a missile attack or artillery bombardment. It did not say when he was killed.
Nawar al-Saheli, a Hezbollah member of Lebanon's parliament, said Israel was behind the killing.
"This is an open war and we should not preempt the investigation but certainly Israel is behind this," he told the Hezbollah-controlled al-Manar TV station. "The resistance will carry out its duties at the appropriate time."
The Lebanese TV station al-Mayadeen reported Badreddine had been killed in an attack by Israel, which has struck Hezbollah targets in Syria several times since the conflict began in 2011.
There was no immediate response from Israel, which deems Hezbollah its most potent enemy and worries that it is becoming entrenched on its Syrian front and is acquiring more advanced weaponry.
Hezbollah, a political and military movement which is Lebanon's most powerful group, has grown stronger since forcing Israel to end its 22-year occupation of southern Lebanon in 2000. The sides fought a 34-day war in 2006, their last major conflict.
When asked by an interviewer on Israel Radio about possible Israeli involvement, cabinet minister Zeev Elkin, a confidant of Prime Minister Benjamin Netanyahu, declined to comment.
Yaakov Amidror, a former national security adviser to Netanyahu, said Badreddine's killing was good news for Israel but stopped short of saying Israel was responsible.
"We don't know if Israel is responsible for this," he told Israel's Army Radio. "Remember that those operating in Syria today have a lot of haters without Israel."
"But from Israel's view, the more people with experience, like Badreddine, who disappear from the wanted list, the better," he said.
A U.S. Department of the Treasury statement detailing sanctions against Badreddine last year said he was assessed to be responsible for the group's military operations in Syria since 2011, and he had accompanied Hezbollah leader Sayyed Hassan Nasrallah during strategic coordination meetings with Assad in Damascus.
Announcing his death, Hezbollah cited Badreddine saying he would return from Syria victorious or as "a martyr". A photo released by the group showed him before his death, smiling and wearing a camouflage baseball cap.
Hezbollah's al-Manar TV said he would be buried at 5:30 p.m. (1430 GMT) in the southern suburbs of Beirut.