A statement by the coup leaders published by the state news agency said Colonel Ely Ould Mohamed Vall was "president" of the military council which toppled President Maaoya Sid'Ahmed Ould Taya.
The Military Council for Justice and Democracy had earlier announced the coup in a statement run by the state news agency.
"The armed forces and security forces have unanimously decided to put an end to the totalitarian practices of the deposed regime under which our people have suffered much over the last several years," the statement said.
The council said it would exercise power for two years to allow time to put in place democratic institutions.
Pledge for democracy
Vall, 55, had served as the national police chief since 1987. Known for being calm and tight-lipped, he was considered a close confident of Taya for more than two decades.
"The armed forces have unanimously decided to put an end to the totalitarian...regime under which our people have suffered much"
Military council statement
The military statement also identified 16 other army officers who were members of the council.
It pledged to "establish favourable conditions for an open and transparent democratic system on which civil society and political players will be able to give their opinions freely".
"This council pledges before the Mauritanian people to create favourable circumstances for an open and transparent democracy," it said.
Top establishment involved
An opposition leader and a military source said they believed the head of the presidential guard, Colonel Mohamed Ould Abdel-Aziz, was involved in the coup d'etat.
There were reports that some senior members of the military had been arrested but it was not possible to confirm them.
Hundreds of people took to the streets of capital Nouakchott, shouting and honking car horns in celebration after the coup announcement, witnesses said.
Convoys of cars with people hanging out of them shouting "praise be to God" and making victory signs paraded down one of the main sand-blanketed avenues.
Freedom from dictatorship
"There was no democracy here, there was just slavery. We have been freed from a dictatorship," said one man, Bilal, aged around 45, watching from a side street.
"It's like we've been imprisoned for decades. I'm so happy. Change is good. We've been disappointed by the regime," shouted Mohammed, in his early 20s, as he ran down the street.
Taya (R) was greeted by the Niger
president at Niamey airport
Police armed with batons patrolled other parts of the city but appeared to be maintaining a low profile, while some streets around key buildings were still sealed off by soldiers, residents said.
Earlier on Wednesday, troops led by the presidential guard took over key buildings in Nouakchott, including the military headquarters, the state radio and television offices, the presidential palace and ministries.
They acted while Taya was in Saudi Arabia for the funeral of King Fahd.
He was later reported to have landed in Niamey, capital of Niger and was received by Niger's President Tandja Mamadou and government ministers.