Lt Gen Gadi Eisenkot said Israeli intelligence had similarly concluded that Mustafa Amine Badreddine was assassinated by his own men.
He was killed by a blast near Damascus, which the militant Lebanese Shia group blamed on Sunni extremist rebels.
Badreddine was believed to have run the group’s operations in Syria since 2011.
Hezbollah is heavily involved in the country’s civil war, deploying thousands of fighters in support of President Bashar al-Assad.
The report said Hassan Nasrallah was put under pressure to remove Badreddine by Maj Gen Qasem Soleimani, head of the Iranian Revolutionary Guards’ elite overseas operations arm and a key adviser to the Syrian military.
Israeli intelligence believes Badreddine was in conflict with Iranian military commanders there, according to the Associated Press news agency.
An initial report by Lebanon’s al-Mayadeen TV said the 55 year old had died in an Israeli air strike. But a later statement by Hezbollah published by its al-Manar news site did not mention Israel. Israel did not comment on any alleged involvement.
Israel is believed to have carried out multiple air strikes on weapons convoys in Syria destined for the group, and to have killed senior Hezbollah operatives, though it does not comment on such claims.
On Tuesday, Gen Eisenkot said the Arab media reports that Hezbollah had killed Badreddine matched the “intelligence we have”.
He added that the killing reflected “the depth of the internal crisis within Hezbollah”.
Badreddine was a cousin and brother-in-law of Imad Mughniyeh, who was the commander of Hezbollah’s military wing until his assassination by car bomb in Damascus in 2008 – reportedly the result of a joint operation by Israel’s Mossad spy agency and the US Central Intelligence Agency.
Badreddine himself was charged by prosecutors at The Hague with masterminding the assassination of former Lebanese Prime Minister Rafik Hariri, who was killed by a huge car bomb blast in Beirut in February 2005.