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Al-Sissi, whose current term ends in April, is widely expected to win. The polls will be held amid an economic crisis, record inflation and a sharply depreciated local currency.
"I have decided to nominate myself to complete the dream during a new presidential term," he said, making the announcement during a televised speech.
Pro-government televisions showed thousands of Egyptians celebrating afterwards, after following his speech in several cities on outdoor screens.
Al-Sissi also said he "was extremely happy with the diversity of candidates" and said that he respected them.
Several leaders in political parties loyal to al-Sissi have announced their intention to stand for president.
Opposition politician Ahmed al-Tanatawi, an ex-lawmaker, also said he will run, and accused security agencies of arresting some of his supporters.
The election will be held over three days from Dec 10-12, with Egyptians living abroad able to cast their ballots from Dec 1-3.
Candidacy registration will open on Oct 5.
Around 65 million Egyptians are eligible to vote, according to Egyptian media.
In 2013, the army led by al-Sissi deposed Egypt's democratically elected but divisive Islamist president Mohammed Morsi.
Al-Sissi first took office in 2014 and was re-elected in 2018.
If he wins, he would rule the country for a six-year term.
Egypt has seen a crackdown on freedom of expression under al-Sissi, with hundreds of activists and Islamists imprisoned or forced into exile, which has triggered outcry from human rights advocates.
In recent months, the government has released dozens of detained dissidents - AFP