"The blockage is lifted," said an official in the delegation of Lebanese President Michel Aoun, who held talks in the Saudi capital with King Salman.
"It's finished. There is truly a change. But when and how, we have to wait to see," the official said, adding "a new page" had been turned and the aid was "going to move."
In February, the kingdom halted the military aid programme to protest what it said was "the stranglehold" which the Iran-backed Shiite militant group Hezbollah had on the Lebanese state.
It aims to ensure stability in Lebanon as it is weakened by internal divisions and threatened by jihadists and the conflict in neighbouring Syria.
Salman's son, the powerful Defence Minister and Deputy Crown Prince Mohammed bin Salman, will discuss with his Lebanese counterpart how to move forward with the package, said the official, who asked for anonymity.