During his time at Stamford Bridge, Carvalho - who won the Champions League with Porto back in 2004 - also won the FA Cup three times, the League Cup twice and the Community Shield twice.
Carvalho played more than 200 games for Chelsea, scoring 11 goals and he is confident he will have no trouble adapting his game to the Spanish league.
"The speed of the game is different here to England, where the game is quicker," Carvalho explained.
"I think it was harder for me to adapt to English football than it will for me to adapt to the Spanish game because it is so similar to the Portuguese league."
He becomes Real's fifth signing of the summer, following Argentine Angel di Maria, Spanish duo Pedro Leon and Sergio Canales and Germany World Cup star Sami Khedira.
But the defender is aware his experience could be vital to the Spanish side after the departures of club legends Raul and Guti following the team's failure to win La Liga under previous manager Manuel Pellegrini.
"I have spoken with Mourinho about my role as a senior player here on the pitch," said Carvalho.
"A lot of important players have left this year. I want to help Madrid win as much as I can."
statement on the Spanish club's website began:
"Best known for his perfect positioning, his foresight and his ability to advance the ball out of the first third, Ricardo Alberto Silveira Carvalho joins Real Madrid at the age of 32 and with 19 titles to speak of."
Carvalho is the fifth player to leave the Stamford Bridge club this summer after Joe Cole, Michael Ballack, Juliano Belletti and Deco.
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