Official results show close to 97 percent of the votes cast chose the constitution which will set the tone for major democratic reforms.
Head of the military junta Ely Ould Mohamed Vall described the adoption of the supreme law as a "leap ... marking a major event in the history of Mauritania and a decisive stage of the democratic transition process."
The acceptance of the constitution - in what observers declared free and fair polls - gives a boost to the 17-member Military Council for Justice and Democracy which is trying to steer the country toward democracy after two decades of authoritarian rule.
Taya expressed his government's determination "to resolutely continue the political, economic and social reforms and to organise the next electoral exercise according to the transitional calendar".
Observers happy with vote
Observers from the African Union and the Arab League said they were happy with the way the vote went, noting a "good atmosphere" and a "strong mobilisation of voters".
Two African non-governmental organizations recognized by the AU also noted in a joint statement that the vote was "transparent, free, equitable and peaceful".
The Interior Minister Mohamed Ahmed Ould Mohamde Lemine said the 'yes' vote carried the day after only 1.42 percent of those who voted rejected the constitution. Another 1.61 percent of
the votes were invalid. Turnout was 76.51 percent, he said.
Close to a million people were eligible to cast ballots in the referendum.
Series of polls to be held
The new constitution, replacing a 1991 one, had already won the backing of most political players and local civic and political rights groups.
Its approval has set into motion a series of polls to take the country - which has not had a leader come to power through elections since independence from France 40 years ago - to democracy.
Municipal and legislative elections are to be held in November, followed by polls in 2007 to elect senators and a president.
Under the new constitution, the presidency is to be limited to a maximum of two five-year terms, while previously presidents have been able to serve a six-year term of office renewable indefinitely.
Ould Taya, who took office after a coup in December 1984, had subsequently been elected to three six-year terms.
Future heads of state will take an oath not to revise or back any efforts to change the law with respect to presidential terms.
It also provides for a presidential regime that gives the head of state major powers, including the appointment of the prime minister, though the parliament can vote no confidence in the government or censure it.
The junta leader, who along with his council are not taking part in any of the upcoming polls, are to step down after the transition which culminates in presidential polls in March next year.
Only two small parties, the Alliance for Justice and Democracy and the Party for the Third Generation, as well as an exiled group campaigning for the rights of black Mauritanians, called for a boycott of the vote.