He then went through a full medical before giving an interview to BJK TV, the official TV station of the Istanbul-based club.
Defender Pepe, who spent 10 years at Real Madrid, has now left the club as a free agent.
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. He could not play in the 2017 Champions League final against Juventus.
Do you think Pepe could have signed for a bigger club?
Samsung is investing $32 billion to keep lead in chips
Samsung will make a huge investment towards the expansion and upgrade of its memory chip and smartphone business in South Korea. So, in 2016, the business for the production of chips provided 46.5% of operating profit of Samsung .
Joining Pepe at the signing ceremony on Wednesday, Beşiktaş Chairman Fikret Orman said Pepe had a significant career and had always been in their sights.
The 34-year-old was a mainstay in the Madrid side after joining from Porto in 2007, appearing 334 times for the club.
It will be interesting to see what Real Madrid do in this transfer window, having already lost three players this season with the likes of Diego Llorenthe, Mariano Diaz and now Pepe.