The Brazilian has one season left on his deal at Real with the option of another depending on the number of games he plays next season.
“The left back, who is at the pre-season training camp in Austria, will complete his contract with the side,” Real said in a statement on their website issued yesterday.
The 33-year-old met Real sports director Predrag Mijatovic on Tuesday after being convinced he was wanted by new coach Fabio Capello.
“I spoke with Mijatovic and told him about the offers I had from Chelsea and Fenerbahce. We haven’t changed anything with regard to my contract. I want to continue here,” Roberto Carlos added.
“Knowing Capello and Mijatovic, who I played with at Real, was important, but it’s my family’s decision that carried most weight.”
He had hinted that it was time to move on at the end of last season, saying he had received an offer from Chelsea of a three-year contract.
Turkish side Fenerbahce, now managed by Brazilian Zico, were also reported to be interested in him.
Roberto Carlos, who has won three Champions League titles with Real, retired from international football after the World Cup in Germany.