Colonel Vall, 55, has become head of the 17-member Military Council for Justice and Democracy, the council said in a written statement.
Mauritanian army troops, including members of the presidential guard, seized control of the state radio and television in the capital early Wednesday while President Maaouya Ould Sid'Ahmed Taya was out of the country.
However, the international community has strongly condemned a coup that ousted the regime of the oil-rich northwest African country of Mauritania.
Deposed leader Ould Taya had been in Saudi Arabia attending the funeral of King Fahd and was prevented from returning home when the military closed down the Nouakchott airport.
Taya, who had ruled Mauritania since staging a bloodless coup in 1984, landed in Niger where he was received by Nigerien government officials.
During his 21-year reign, Taya had foiled many coup attempts and cracked down ruthlessly against opponents.