The Colombia striker left Galatasaray last week to sign for Rayo.
"It is an opportunity for my career, I am very happy to join this institution. It is a place where they will give me all the confidence to be able to give my best and be part of a team with a very nice spirit," said Falcao.
"I know several players from there, they have transmitted to me what the dressing room, the coaching staff are like, so I feel very proud to be part of this club and to return to a league that I already know, which is very competitive and surely it will allow me to continue growing."
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