Abdel Aziz was handed another five years with 82 percent of the vote on June 21 in polls boycotted by much of the opposition.
He was cheered by thousands at the Olympic Stadium in the capital Nouakchott as he vowed to address the problems of the northwest African nation's poor and "fight corruption and mismanagement" yesterday.
He also pledged to tackle racism and extremism, and said he would take on terrorism and organised crime by strengthening the army.
The heads of state of the Gambia, Guinea Bissau, Mali, Senegal and Chad attended the ceremony as well as diplomats and dignitaries from various other countries.
Abdel Aziz, a former general, seized power in an August 2008 coup and won disputed elections the following year.
He campaigned strongly on his success in fighting armed groups linked to Al-Qaeda at home and in neighbouring Sahel nations.
Following his victory, the 57-year-old pledged "to be the president of all Mauritanians and to guarantee the rights of all citizens".