The Dutch winger has reportedly reached an accord with the Turkish giants over a four-year deal, thereby putting an end to speculation surrounding his future
According to NTVspor, the 25-year-old, who was released by Real Madrid earlier in the summer, will put pen to paper on a four-year contract with the Super Lig outfit.
Drenthe moved to the Santiago Bernabeu from Feyenoord in 2007 after playing a starring role in the Netherlands' successful European Under-21 Championship campaign.
However, he failed to establish himself under a string of coaches in the Spanish capital, despite early promise, and was farmed out on loan to Hercules and Everton.
He was unable to earn a permanent transfer with either side, and had been allowed to look for a new club since the end of 2011-12 following the expiration of his contract.
But it is Besiktas who have seemingly won the race for the left-sided player, beating off reported interest from Manchester City, Galatasaray and AC Milan.