Ayatollah Khamenei issued a message of condolence on Saturday, two days after the former VP died in the capital Tehran.
The leader condoled with his family and hailed Davoodi for his good performance while in office.
Davoodi was an Iowa State University graduate. He served under former president Mahmoud Ahmadinejad from 2005 to 2009.
Davoodi was also a member of the Expediency Council and a tenured professor of Shahid Beheshti University in Tehran.
He passed away aged 72 and was laid to rest in the capital’s Behesht-e Zahra Cemetery on Saturday.
The cause of his death was not revealed.