Khaled Bahah, who is in Saudi Arabia, said his government would work to restore basic services there.
Aden has for months seen heavy fighting between rebels and loyalist forces backed by Saudi-led air strikes.
The government fled from its stronghold in Aden in March as the Houthis pushed towards the provincial capital.
A major offensive to drive the Houthis out of Aden was launched earlier this week.
On Thursday, several minister from the exiled government of President Abdrabbuh Mansour Hadi returned to the country for the first time since taking refuge in Riyadh.
They flew by helicopter to a military base on the outskirts of Aden city with instructions to prepare for the government's return, officials said.
In a statement on his Facebook page, Khaled Bahah said: "The government announces the liberation of the province of Aden on the first day of Eid al-Fitr which falls on July 17.
"We will work to restore life in Aden and all the liberated cities, to restore water and electricity."
Aden - the country's main port and second city - has been devastated by weeks of clashes and air strikes.
The losses in Aden represent the biggest setback for the Houthis since Sunni power Saudi Arabia launched a coalition air campaign against them on 26 March.
Mr Hadi had taken refuge there after the Houthis consolidated their control of the capital, Sanaa.
The Saudis say the campaign is aimed at forcing the rebels - who they say are armed by regional Shia rival Iran - to retreat and to restore the exiled government.
Iran denies backing the Houthis militarily.
The UN says more than 3,200 people, half of them civilians, have been killed in air strikes and fighting on the ground in the past 15 weeks.
Another one million civilians have been displaced by the conflict and more than 80% of Yemen's 25 million people now need some form of humanitarian aid.
Yemen's southern province of Aden has been "liberated" from Houthi rebel forces, the country's exiled vice-president has declared.