President Abdelaziz was shot in the arm by a Mauritanian army soldier in what the government said was an accident.
He had been in France for the last six weeks receiving treatment.
Thousands of people gathered at the airport to greet the president on his return to the capital Nouakchott.
Large crowds also lined the route between the airport and the presidential palace.
Reporters present said the 55-year-old leader appeared to be in good health, and waved to crowds from his car, though he gave no statement.
The soldier responsible for shooting the president told Mauritanian television last month that he had fired on a car that appeared suspicious while guarding a military base outside Nouakchott, failing to realise that one of the occupants was the president.
President Abdelaziz seized power in a coup in 2008, in a country with a long history of coups.
He won a presidential election a year later and is seen by Western governments as a bulwark against Islamists in the region.