Fenerbahçe shared an Instagram picture of Nani boarding a private jet ahead of his trip to Istanbul earlier.
Large crowds of Fenerbahçe supporters have gathered at the airport to greet the Portuguese international.
Nani will undergo a medical before signing for the Yellow Canaries on a four-year deal.
The 28-year-old winger is expected to sign a four-year deal worth €3.975 million, according to a close Turkish-football.com source.
Nani will become the Yellow Canaries seventh transfer of the transfer window after Simon Kjaer, Fernandao, Şener Özbayraklı, Abdoulaye Ba, Fabiano and Josef De Souza.
The four-times Premier League champion will also become the third Portuguese international at the Yellow Canaries alongside Bruno Alves and Raul Meireles.