The announcement is an indication of a growing feud between Israel and Hezbollah, an Iranian-backed group sworn to Israel's destruction.
Hezbollah has over 100,000 rockets and missiles aimed at Israel and they are seen as a powerful enemy of the Jewish State. But Israel believes the group has been weakened and demoralized after fighting alongside Syrian President Bashar Assad's forces in Syria.
Eisenkot said that the death of Badreddine illustrates "the depth of the internal crisis within Hezbollah," and also said that it reflected "the extent of the cruelty, complexity and tension between Hezbollah and its patron Iran."
One Israeli official said his country believes that the order to kill Badreddine was given by Hezbollah's leader, Hassan Nasrallah.
Israeli intelligence believes Badreddine had been feuding with Iranian military leaders in Syria over the numerous losses his fighters suffered in battle. Both Iran and Hezbollah are backing Assad's government forces.
Hezbollah had no comment other than to say that Badreddine was killed as a result of insurgent shelling in Syria.
Badreddine was considered Hezbollah's top military official and was among five members on trial in absentia in the Netherlands for the bombing that killed Lebanese Prime Minister Rafik Hariri along with 21 others in Beirut in 2005.
Hezbollah doesn't want a confrontation with Israel right now because it's bogged down in the Syrian fighting and has lost hundreds of militants.