Mr Nasrallah said the mountainous border area of Qalamoun would be the target, but did not specify when.
He said Syrian rebel forces, which frequently target Hezbollah across the border, posed an unacceptable threat.
Hezbollah, an ally of Syrian President Bashar al-Assad, has sent hundreds of fighters to join the Syrian civil war.
The Qalamoun area, which straddles the Syria-Lebanon border, is porous and largely unpatrolled.
In a televised address on Tuesday, Mr Nasrallah said cross-border attacks by militants from the al-Qaeda affiliated al-Nusra Front posed an unacceptable threat to Lebanon's security and required "radical treatment".
"The (Lebanese) state is not able to address this issue... so we will proceed with the necessary treatment and assume the responsibility and consequences," he added.
He declined to say when the operation would begin adding: "Even when we start, we will not issue a statement. When we begin, the operation will speak for itself."
Most of the border region was recaptured from al-Nusra Front and Islamic State forces last year after a major assault by Syrian government troops, backed by Hezbollah fighters.
However, jihadists entrenched there have continued to launch attacks, with clashes reported as recently as Tuesday.
Lebanese officials say several hostages, including soldiers and police officers, are still being held after being seized along the border last year.
Fighting from Syria frequently spills over into neighbouring Lebanon, with cross-border clashes and bombings.
The conflict in Syria has also exacerbated existing tensions in Lebanon - which suffered its own civil war between 1975 and 1990 - and made Hezbollah and areas which support it targets for Sunni militant bomb attacks.
Hezbollah leader Hassan Nasrallah says his Lebanese Shia group will launch an attack inside Syria on Sunni militants fighting for the al-Nusra Front.