Adel, 68, announced his withdrawal from the race four days before the vote, without elaborating on the reason.
He was the parliament speaker from 2005 to 2008.
He is currently a member of the Expediency Council and is considered a strong conservative voice.
Adel's daughter is married to one of the supreme leader's sons.
Adel, who is a close confidant of Khamenei's, has held a number of government posts, including deputy minister of Islamic guidance, deputy minister of education, and head of Iran's Academy of Persian Language and Literature.
Adel, who was born in Tehran, has a doctorate in philosophy from Tehran University, where he holds a position in the philosophy department.