Sabbahi finished third in the 2012 presidential race, behind winner Mohamed Morsi and Ahmed Shafiq.
He made the announcement on Saturday at an event in Cairo, Ahram Online reported, and is the first to confirm that he will run in the election.
The military's Abdel Fattah al-Sisi is the favorite in the elections, but hasn't officially announced his candidacy.
He has grown popular since the ousting of Morsi in July.
Elections are set to take place April 18.