Iran moved up six places in medal table compared to the previous edition held in Tokyo.
The US topped the medals table at the Paris Olympics with 40 golds after the final title was decided on Sunday, finishing above China only by virtue of their 44 silvers.
China, who was the last team apart from the US to top the standings when it did it on home soil at the 2008 Beijing Games, also won 40 golds but managed only 27 silvers.
The US also won most total medals with 126 to China's 91.
Iran sent 41 athletes in 14 sports to Paris.
Saeid Esmaeili in the men’s Greco-Roman 67kg, Mohammad Hadi Saravi in the men’s Greco-Roman 97kg and Arian Salimi in the men’s taekwondo +80kg claimed three gold medals for Iran.
Alireza Mohmadi in the men's Greco-Roman 87kg, Nahid Kiani in the women’s taekwondo 57kg, Mehran Barkhordari in the men’s taekwondo 80kg, Amir Hossein Zare in the men’s freestyle 125kg, Rahman Amouzad in the men’s freestyle 65kg and Hassan Yazdani in the men's freestyle 86kg won six silver medals.
Amin Mirzazadeh in the men's Greco-Roman 130kg, Mobina Nematzadeh in the taekwondo women's 49kg and Amir Ali Azarpira in the men's freestyle 97 kg seized three bronzes.