Warfare between the erstwhile allies has torn densely populated Sanaa for days, with Houthi fighters seizing control of much of the capital and on Monday blowing up Mr Saleh's house.
Speaking later on television, President Abedrabbo Mansour Hadi, the leader of the internationally recognized government, called on Yemenis to unite against the Huthis.
The Houthi-run Masirah TV announced the death of the "leader of the traitors" on Monday, referring to Saleh, who until last week was in a fragile alliance with the rebels.
The death is expected to have a major impact on the Iranian-Saudi proxy war taking place in Yemen, the poorest nation in the Arab world.
A video showed Saleh's body, motionless, blood staining his shirt and a gaping wound In his head. The new situation is critical and unsafe, and requires the interference of the Yemeni army and coalition forces in Sanaa, as well as working with Saleh's forces, which are still in shock.The people of Sanaa and the forces of the late Saleh have a great interest in fighting a war to reclaim their city from Houthis.
Saleh's General People's Congress party confirmed his death and blamed the rebels.
Houthi went on to blast Saleh for betraying the loyalty of those he had worked with and claimed the ordinary people of the capital could not understand how he had changed sides after three years of denouncing the Saudi-led coalition.
Homicide investigation underway following disappearance of NC 3-year-old
Mariah was last seen Sunday night when her mother, Kristy Woods, put the girl to bed, according to the sheriff's office. Authorities have arrested a man in connection with the disappearance of a 3-year-old North Carolina girl.
It was a bitter end for the former president who had ruled the north of Yemen and then a united north and south for almost 34 years.
Saleh, who was Yemen's president for 33 years until he stepped down in 2012 amid an Arab Spring uprising, was killed Monday by the Shiite rebels whom he'd once allied with in hopes of a return to power but then turned against in recent months.
The staement read "Saleh and his supporters have been killed by Houthis rebels".
The coalition will either have to continue waging a grinding war, possibly trying big offensives against Houthi-held areas at the risk of high civilian casualties, or offer compromises to bring the powerful Houthis to the negotiating table.
Saleh on Saturday, December 2, announced he was open to talks with Saudi Arabia and its allies on condition they ended their crippling blockade of Yemen's ports and airports.
In March 2015, a Saudi-led coalition intervened to reinstate Hadi's government.
In a televised speech on Monday, Huthi made no mention of Saleh's death but expressed his satisfaction at the day's events. Saudi-led aircraft continued to fly overhead.