The medical took place at 10:00 local time at the Liv Hospital in Ulus, Istanbul.
Nani arrived at the Sabiha Gökçen airport in Istanbul on a private jet yesterday and was greeted by hundreds of Fenerbahçe fans who welcomed him to the country.
The Portuguese international is expected to sign a four-year deal worth €3.975 million, according to a close Turkish-football.com source.
Nani has become the Istanbul giants seventh transfer of the transfer window after Simon Kjaer, Fernandao, Şener Özbayraklı, Abdoulaye Ba, Fabiano and Josef De Souza.
The four-time Premier League title holder will also become the third Portuguese international at the Super Lig outfit alongside Bruno Alves and Raul Meireles.