For years in the shadow of Istanbul rivals Fenerbahce and Galatsaray, the Black Eagles have won the Turkish Super Lig title for the last two seasons.
The 34-year-old Brazilian-born defender Kepler Laveran Lima Ferreira joined Real from Porto in 2007 for 30 million euros ($34 million), winning the La Liga title in his first campaign.
With Turkey's only automatic Champions League berth in their possession, Beşiktaş hope for drastic improvement on their group-stage exit last time round.
"I spent 10 wonderful years at Real Madrid", Pepe explained. The veteran centre-back was heavily linked with a transfer to Paris Saint-Germain and even had a medical with the Ligue 1 giants.
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We now have the president encouraging violence against the media. "If anything, quite the contrary". Prior to it, Trump took aim at the press during an event to commemorate the American independence.
Do you think Pepe could have signed for a bigger club?
Though Pepe made only 18 appearances for Real Madrid last season due to injuries, he was a key member of the Portuguese national team that won the European Championship title a year ago.
Pepe's time at Madrid will be considered a success, despite a controversial incident in April 2009 where he savagely kicked Getafe player Javi Casquero and was sent off.
He also has the honour of being named man of the match as Portugal beat hosts France in extra time in the Euro 2016 final.