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 broadcasters showed thousands of Egyptians celebrating after following his speech in several cities on outdoor screens.
Sisi also said he "was extremely happy with the diversity of candidates" and said that he respected them.
Several leaders in political parties loyal to Sisi have announced their intention to stand for president.
Opposition politician Ahmed al-Tanatawi, a former MP, also said he will run and accused security agencies of arresting some of his supporters.
The election will be held over three days on December 10-12, with Egyptians living abroad able to cast their ballots on December 1-3.
Candidacy registration will open on October 5.
About 65 million Egyptians are eligible to vote, according to Egyptian media.
In 2013, the army led by Sisi deposed Egypt's democratically elected but divisive Islamist president Mohamed Morsi.
Sisi first took office in 2014 and was re-elected in 2018.
If he wins, he would rule the country for a six-year term.
Egyptians have experienced a crackdown on freedom of expression under Sisi, 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.
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