The 32-year-old center will join Shahrdari to strengthen the team in the Iranian Basketball League.
Shahrdari sits eighth in the table.
Akingbala is 2.09m tall and he can play both power forward and center positions.
Akingbala went undrafted in the 2006 NBA draft. In July 2006, he joined the Boston Celtics for the 2006 NBA Summer League.
He later signed with the Celtics, but they waived him in October 2006.
Akingbala then joined the Los Angeles D-Fenders of the NBA D-League.
Financial details of the deal have not been revealed.