Members of his delegation told reporters that Taya, who was offered asylum by the Gulf Arab state, was staying at a Doha hotel with his wife and four children.
Taya and his family left Gambia on Sunday.
Qatar has offered asylum to several public figures, including Algerian Islamist opposition leader Abassi Madani and exiled Chechen rebel leader Zelimkhan Yandarbiyev, who was
killed in a Doha car bomb attack last year.
A 17-member military council led by some of Taya's closest aides seized power in the Islamic republic that straddles black and Arab Africa on 3 August, while the president was out of the country attending the funeral of Saudi Arabia's late king Fahd.
The council has pledged elections within two years.
The coup won widespread support in Mauritania, with jubilant residents taking to the streets to celebrate the end of Taya's 21-year rule.
The US and the African Union among others initially condemned the coup, but have since softened their stance.
Washington, in particular, has said it is prepared to work with the military government if the new rulers show they can keep their promise of polls.
Taya has urged soldiers to resist the country's new leadership and vowed to return to his home country soon, although his words did not appear to be taken seriously by residents and officials in Mauritania's capital Nouakchott.