He helped Real win five La Liga and three Champions League titles.
"They're a lot of years and many (were) complicated but in the end I managed to achieve the most important things," added Guti. "So many years here... an unforgettable stage (of my life)."
Along with Raul, who will make an emotional exit from the Bernabeu on Monday at a farewell media conference amid reports suggesting the 33-year-old will join German club Schalke, Guti is an iconic figure at Real.
"He is a special player who managed to surprise us in every game," said managing director Jorge Valdano, who gave Guti his first call-up as coach. "A true Madridista. Today is a sad day because one of our own is leaving."
Should Guti move to Besiktas he will be coached by his former Real Madrid boss Bernd Schuster.
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