Officials from Mr Saleh's General People's Congress party said he died in an attack south of the capital, Sanaa.
The Houthis' leader hailed the news as a "great and significant occasion".
Abdul Malik al-Houthi said it had foiled a "conspiracy" by a Saudi-led coalition backing the government, to whom Mr Saleh had made peace overtures.
Until last week, Mr Saleh's supporters had been fighting alongside the Houthis in a war against Yemen's current president, Abdrabbuh Mansour Hadi.
But longstanding political tensions and a dispute over control of the main mosque in the rebel-controlled capital, Sanaa, triggered fierce clashes that have left more than 125 people dead and 238 wounded since Wednesday night.
On Saturday, Mr Saleh offered to "turn a new page" with the Saudi-led coalition backing Mr Hadi if it stopped attacking Yemen and ended its crippling blockade.
The coalition and Mr Hadi's government welcomed the comments. But the Houthis accused Mr Saleh of staging a "coup" against "an alliance he never believed in".
Overnight, Sanaa was rocked by coalition air strikes on Houthi positions and clashes on the ground involving heavy weapons as the conflict between the rivals escalated. Aid workers said the violence had trapped civilians inside their homes.
Hakim Almasmari, editor of the Yemen Post newspaper, told Al Jazeera TV that Houthi fighters had opened fire on Saleh's convoy as it passed through a checkpoint on the way from Sanaa to his hometown of Sanhan.
A video circulated on social media showed the body of a man resembling Mr Saleh with a severe head wound. It was being carried on a red blanket by several armed men shouting "Praise be to God!" and "Hey Ali Affash!" - the name of Mr Saleh's clan.
A statement by the Houthi-run interior ministry, carried by rebel-aligned media, announced "the killing of the leader of treachery and a number of his followers".
The death of Ali Abdullah Saleh at the hands of the Houthis now makes any immediate prospect of peace for Yemen even less likely.
The alliance between Saleh's forces, mainly his Republican Guard who remained loyal to him after he was ousted in 2011, and the rebel Houthis from the north lasted three years.
Together, they were strong enough to hold on to Sanaa and repel the forces of Yemen's internationally-recognised government and its Gulf Arab allies from much of the mountainous north.
Cracks had recently been showing in that alliance, with Mr Saleh turning his back on the Houthis and hinting at a deal with the Saudis. He appears to have paid for it with his life, meeting a similarly ignominious end as that suffered by Libya's Muammar Gaddafi in 2011.
Mr Saleh's supporters, who are well-armed, will now seek revenge, probably supported by the very Saudi air strikes that have previously been targeting them.
Officials from Mr Saleh's General People's Congress later confirmed that he had been killed in an incident outside Sanaa.
"He was martyred in the defense of the republic," Faiqa al-Sayyid, a leader of the party, was quoted as saying by the AFP news agency.
Mr Saleh came to power as president of North Yemen in 1978. When the country was united with South Yemen in 1990 he became president of the new republic.
The Houthis, who champion Yemen's Zaidi Shia minority, fought a series of rebellions against Mr Saleh between 2004 and 2010. They also supported an uprising in 2011 that forced Mr Saleh to hand over power to his deputy, Mr Hadi.
Mr Saleh's supporters formed a surprise alliance with the Houthis in 2014, when they seized Sanaa amid widespread disillusionment at the political transition and Mr Hadi's failure to tackle corruption, unemployment and food insecurity.
In early 2015, the allies ousted Mr Hadi, forcing the president to flee initially to the second city of Aden and then to Saudi Arabia. The Saudi-led coalition responded by launching a military campaign to restore Mr Hadi's government.
Since then, more than 8,670 people have been killed and 49,960 injured.
The conflict and a blockade by the coalition has also left 20.7 million people in need of humanitarian aid, created the world's largest food security emergency, and led to a cholera outbreak that is thought to have killed 2,211 people since April.