The Madrid-born forward became the La Liga club’s all-time top goalscorer with 228 strikes in 550 league appearances for Los Blancos.
The 33-year-old, who won six La Liga titles and enjoyed three Champions League successes during his time at the BernabÃƒÂ©u, has expressed his sadness at leaving Madrid.
“It’s a hard day for me,” said the former Real Madrid captain at a press conference on Monday.
“Football has been my life and Real Madrid my home and together we have lived unique moments.
“I feel like a footballer still and I will keep on playing, but I will always be loyal to Real Madrid. I have tried to give everything in my time here.”
RaÃƒÂºl has been linked with a move to German side Schalke, but a deal has yet to be confirmed.
“A new period starts today,” he continued. “I have been happy at Real Madrid and I will always be willing to help the club in whatever it needs.
“In a few days I will know whether I’ll be going to the Bundesliga (or to England).”
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