The footage broadcast by Al-Jazeera news channel follows several days of online chatter over a split between Al-Qaeda and its Syria affiliate, a main rival of the Islamic State (IS) jihadist group from which it wants to distance itself as a target of foreign air strikes.
Appearing in public for the first time, Jolani said Al-Nusra changed its name to Jabhat Fateh al-Sham (Front of the Conquest of Syria) and would unify ranks with other mainstream fighters in Syria.
"We decided to stop operating under the banner of Al-Nusra and to set up a new front, called Jabhat Fateh al-Sham," he said.
Clad in military fatigues and wearing a turban, the bearded Jolani thanked "the commanders of Al-Qaeda for having understood the need to break ties".
And he vowed the new group would "have no links whatsoever with foreign parties".
Analysts said Al-Nusra aims to rebrand and defend itself as it comes under increased pressure after Moscow and Washington agreed to step up joint efforts against jihadist groups.
US Secretary of State John Kerry and his Russian counterpart Sergei Lavrov said last week they had agreed "concrete steps" to save a failing Syria truce and tackle jihadists like Al-Nusra and IS.
But with the amicable break from Al-Qaeda, Jolani "can now call upon a broad spectrum of armed groups in Syria to agree to unite initiatives", said analyst Charles Lister.
"It's also, plain and simple, a recognition of the need to confuse one's enemies, given US-Russian plans to begin military operations" against Al-Nusra, he said.
Washington said it still considers Al-Nusra Front a security threat despite the announcement.
"We certainly see no reasons to believe that their actions or their objectives are any different," said State Department spokesman John Kirby.
"They are still considered a foreign terrorist organisation," Kirby said. "We judge a group by -- by what they do, not by what they call themselves."
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In the brief recording, Jolani, flanked by two bearded men, said the split was aimed at "protecting the Syrian revolution" and to offset any excuse by the international community to target Al-Nusra.
"We hope to form a unified body, based on the shura (Islamic law), uniting the masses of the people of Al-Sham, liberating their lands, giving victory to their faith and upholding their testimony of faith," he said.
Al-Nusra is already a leading member of the Army of Conquest, an alliance of Islamist and rebel fighters, that controls the northwest province of Idlib.
Lister said that one of the men sitting beside Jolani was Al-Qaeda veteran leader Ahmed Salameh Mabrouk.
"Al-Qaeda is playing a critically important role in shaping this development and their thinking and strategising will remain crucial for this new Jabhat Fateh al-Sham movement," he said.
"It will still oppose the most moderate of opposition groups in Syria; it will still be viciously sectarian, and it will still ultimately seek the establishment of an Islamic emirate in Syria and the potential launching of external attacks on the West."
'For the good of Islam'
Al-Qaeda, founded by Osama bin Laden and to which Al-Nusra pledged allegiance in 2013, prepared the ground for Thursday's announcement.
"We direct the leadership of Al-Nusra Front to go ahead with what preserves the good of Islam and the Muslims, and protects the jihad of the Syrian people," Ahmed Hassan Abu al-Khayr said in an audio message released online by Al-Nusra.
"We urge them to take the appropriate steps towards this matter," said Abu al-Khayr, identified as the deputy of Al-Qaeda leader Ayman al-Zawahiri.
Al-Nusra emerged in January 2012, 10 months after Syria's conflict began with anti-government protests that were brutally repressed by President Bashar al-Assad's regime.
Unlike the IS group, which opposes all those who fail to swear allegiance, Al-Nusra has worked alongside an array of rebel groups fighting Assad's regime and has popular support.
Analyst Aymenn Jawad al-Tamimi, speaking ahead of Jolani's announcement, said "Al-Qaeda's central leadership endorses the idea of embedding Jabhat al-Nusra more deeply in the Syrian insurgency".
Lister said the split between Al-Nusra and Al-Qaeda had been prompted by the US-Russia agreement to coordinate efforts and target jihadists operating in Syria.
Al-Nusra, which has 7,000-8,000 fighters according to Syria specialist Thomas Pierret, is considered by Washington as a "terrorist" group. It has been the target of both Russian and US-led coalition air strikes.