Prospective contenders had until midnight on Wednesday (0000 GMT Thursday) to register their candidacies.
Aziz led the pivotal country between north and sub-Saharan Africa between 2008 and 2019 and is currently in prison.
On Tuesday, the former leader's spokesman said he was out of the running because he lacked the necessary sponsorships.
But in a surprise move, Aziz headed to the Constitutional Council on the night of the deadline under heavy escort to submit his paperwork, an AFP journalist saw.
The court of appeal had said shortly beforehand that it would authorize his travel for this purpose.
Dozens of Aziz's supporters showed their backing for him nearby but the guards prevented him from speaking.
The former president's legal representative, Seyedna Aly, said that Aziz's candidacy application was still short of sponsors but that, under the rules, he had two more days to complete it.
The Constitutional Council has until May 29 to publish the candidate list.
Several prospective contenders, including Aziz, have denounced the current sponsorship system as playing into the hands of the presidential majority.
It remains uncertain if Aziz will be able to run even if he reaches the required number of sponsorships, as Mauritania's constitution states the president "may only be re-elected once."
Aziz has already served two terms.
The 66-year-old fell into disgrace under his successor and current President Mohamed Ould Ghazouani.
Aziz was sentenced in December to five years in prison for illicit enrichment, but he has denied he used his position to amass a fortune and has always called the charges a conspiracy.
Among the prospective candidates in the June vote are the leader of the Islamist opposition party, Hamadi Ould Sid' El Moctar, and human rights activist Biram Ould Dah Ould Abeid, who came second in the 2019 vote.
Mauritania, which has a population of around 4.5 million, was hit by a series of coups from 1978 to 2008, before the 2019 election marked the first transition between two elected presidents.
While jihadism has spread elsewhere in the Sahel, particularly in neighbouring Mali, Mauritania has not seen an attack since 2011.
Former Mauritania leader to run for president
FILE—Mauritania's out-going President Mohamed Ould Abdel Aziz looks on during the swearing-in ceremony of the newly-elected Mauritania's President at a conference center in Nouakchott, on August 1, 2019.
NOUAKCHOTT—Eight men have submitted their candidacies for Mauritania's June 29 presidential election, including incumbent Mohamed Ould Ghazouani and his jailed predecessor Mohamed Ould Abdel Aziz, who was previously ruled out of the race, according to an AFP count.