According to Sky Sports, the Manchester United striker will travel to Istanbul on Sunday before completing his move to Fener on Monday.
It is believed that the 31-year-old Holland international underwent the initial part of his medical in England on Thursday and will now sign a four-year contract after the two clubs agreed a fee.
Van Persie will join former Red Devils teammate Nani following his move to the Sukru Saracoglu Stadium last week.
Fenerbahce revealed on their Twitter page that talks had started over the transfer of the former Arsenal captain.
Fenerbahce_EN (@Fenerbahce_EN) https://twitter.com/Fenerbahce_EN/status/619154021...">July 9, 2015