Brig. Gen. Ali Qanso told reporters that only 20 square kilometers (12 square miles) remain in the hands of the extremists.
The US-backed Lebanese army launched its operation on Saturday and has since driven out the militants from some 100 square kilometers (62 square miles).
Qanso said no militants have been detained in the operation, adding that many were killed or retreated into Syria.
Earlier today, the army announced it was starting the third phase of the operation, which includes mine clearing to open roads previously controlled by the militants.
The Syrian army and its ally, the Lebanese Hezbollah group, have launched a simultaneous operation to clear IS from the Syrian side of the border in the western Qalamoun mountain range. Hezbollah has been fighting in Syria alongside President Bashar Assad's forces since 2013.
Lebanon's main political factions are sharply divided over the Syrian conflict, with some supporting and others opposing President Bashar Assad.
Lebanese media say the remaining IS-held territory along the border is riddled with caves that the militants could use as hideouts.
Residents of al-Qaa, a village near the border which was attacked by IS militants last year, took to the streets to celebrate news of the army advance. Al-Jadid TV station showed dozens of residents waving Lebanese flags as fireworks cracked above.
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