Ali, 39, pushed incumbent president Sepp Blatter to a second round of voting in May's poll, winning 73 votes, before standing aside in the contest.
He joins Uefa president Michel Platini as confirmed candidates to replace Blatter and lead football's world governing body.
The election is due to be held on 26 February next year.
"This election should be about football, not personal ambition. We have come too far to walk away now," Ali said.
"We must overcome deep-seated corruption but I was not brought up to walk away from a tough fight. This is about right and wrong."
Blatter, 79, triggered next year's election by announcing shortly after winning the last vote that he would resign amid twin criminal investigations into alleged corruption at Fifa.
Seven Fifa officials were arrested in May on charges of racketeering, wire fraud and money laundering.
Former Fifa executive Chung Mong-joon of South Korea has also indicated that he will run in next year's election, as has Liberian FA president Musa Bility.
Referring to May's election, Ali added: "I was the only person who dared to challenge Blatter, I ran because I believe that Fifa needs change.
"I had the courage when others feared. They didn't have the guts to run, but I did."
Prince Ali bin al-Hussein of Jordan has announced that he will stand in the upcoming Fifa presidential election.