Akhtar, 40, who also hosted the ceremony with Shahid Kapoor, bagged the best actor trophy for his powerful portrayal of Singh in the sports drama.
Deepika Padukone, 28, nominated in the best actress category for three of her films, won the award for 'Chennai Express'.
Milkha, who attended the awards gala, got a standing ovation as the biopic on his life received the best picture honour.
Milkha, who was actively involved during the filming of the biopic, got emotional and said, "I am thankful to IIFA for bringing me here and giving me respect. I have cried three-four times in my life... Whenever I see the film I cry. When I was sitting here now I was in tears seeing the love and recognition the film got."
More From This Section
'Bhaag Milkha Bhaag' also won in the best story category along with best supporting actress for Divya Dutta, who played the role of Milkha's sister.
Deepika's 'Ram-Leela' co-star Ranveer Singh handed her the best actress award for her performance in Rohit Shetty's blockbuster.
Deepika was also honoured with the best entertainer of the year award. Veteran actor-politician Shatrughan Sinha was given the Lifetime achievement award for his outstanding contribution to the Indian cinema, while Hollywood star John Travolta received the 'Most Popular All time International star in India' award.