Ilham Aliyev, a 41-year-old oil executive, became the second candidate to make it onto the ballot paper on Friday alongside his 80-year-old father, Haider Aliyev.
Mr Aliyev is said to be critically ill in a Turkish hospital.
It remains unclear which member of the family will run in the election, scheduled for October 15, with the final decision likely to depend on whether Aliyev senior's health will hold up.
Azerbaijan's ambassador to Turkey, Mehmet Nevruzoglu, said on Friday the president is undergoing a check-up, is feeling fine and will return home soon, but the Turkish media has disputed this claim.
Ilham Aliyev, who is vice-president of Azerbaijan's state oil company and head of the country's National Olympic Committee, has said he is only running to bolster his father's campaign for re-election.
"I doubt very much that he (Ilham Aliyev) lives on his deputy's salary alone" -- Anvar Aliyev, opposition party member
Meeting in Azerbaijan's capital Baku, the central election commission voted by 10 votes to five to approve Ilham Aliyev's candidacy after he submitted the necessary documents and 50,000 signatures in his support.
However, his financial declaration caused some raised eyebrows.
According to western diplomats, the Aliyev family controls fabulous wealth.
But the declaration stated his only source of income is his annual salary of $6,700 as a member of parliament, that he owns no car of his own, and lives in a modest-sized house.
"I doubt very much that he lives on his deputy's salary alone," said Anvar Aliyev, a member of the election commission affiliated to an opposition party.
About 15 other would-be candidates, mainly from the opposition, have also submitted applications to be put on the ballot for the election, but none of them has so far been registered.