The soldiers, identified as Aviv Magen, 43, and Etay Azulay, 25, were members of Unit 5515, a combat mobility unit responsible for transporting forces in and out of combat zones.
Two additional soldiers were injured in the incident.
Tensions along the Israeli-Lebanese border were increasing as the Israeli military intensified its airstrikes in Lebanon, while rockets from Gaza and Hezbollah aimed at various locations in Israel.
By early afternoon, Hezbollah militants in Lebanon launched approximately 90 rockets into northern Israel, while Hamas forces in Gaza fired at least 14 rockets targeting central and southern regions, the Israeli military said, Xinhua news agency reported.
Sirens were triggered across the Galilee, Tel Aviv, the southern city of Sderot, and other communities near Gaza. Israel's Magen David Adom rescue service said that three women sustained light injuries - two from a rocket that struck Kfar Chabad near Tel Aviv and one from an overnight strike on Maalot Tarshiha in the north.
The Israeli military said later that its warplanes targeted the launcher in Khan Younis, southern Gaza, used in the attack on Tel Aviv. "During the strike, secondary explosions were observed, indicating the presence of weapons," the military said. Artillery units also struck the launcher in northern Gaza responsible for the subsequent rocket fire on southern Israel.