The push for energy-rich Shabwa came amid heavy air strikes by the Saudi-led coalition battling the Houthi rebels elsewhere in Yemen, including the capital Sanaa.
Yemeni forces have said they are in full control of energy-rich Shabwa province after 10 days of fighting with Houthi rebels.
Yemen's Giants Brigade, a group backed by the United Arab Emirates and also part of a Saudi-led coalition fighting the Iran-aligned Houthis, made the announcement on Monday.
Fighting has intensified since the start of the year, after the coalition sent reinforcements to Shabwa, where Houthi inroads in September had cut off access to the Saudi-backed government's last northern stronghold in Marib.
Marib, in central Yemen, has been the focus of the war for over a year, with the battle for control stymieing United Nations-led peace efforts.
The government holds the province's main city and nearby oil and gas infrastructure.
Marib city is home to 3 million people, including nearly 1 million who fled other parts of Yemen after the Houthis ousted the government from the capital, Sanaa, in late 2014, prompting the coalition to intervene months later.
Intense air strikes
The push in Shabwa came amid heavy air strikes by the Saudi-led coalition battling the Houthis elsewhere in Yemen, including the capital Sanaa.
The rebels have also stepped up their cross-border attacks, using ballistic missiles and explosive-laden drones to target Saudi Arabia.
Yemen's civil war began in 2014 when the Houthis took Sanaa and much of the northern part of the country, forcing the government to flee to the south, then to Saudi Arabia.
The Saudi-led coalition, backed at the time by the US, entered the war months later to try restoring the government to power.
The conflict has since become a regional proxy war that has killed tens of thousands of civilians and fighters.
The war also created the world's worst humanitarian crisis, leaving millions suffering from food and medical care shortages and pushing the country to the brink of famine.
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