The centre-back has moved to Madrid on a free transfer after leaving Malaga, and the Argentinian international has insisted that he feels humble over his move to the Vincente Calderon Stadium.
The 32-year-old told Marca: "I know that I'm joining the best defence in the league and I hope that we can keep that up.
"I will come here with a humble attitude and will contribute what I can. I hope it's a successful year for me and for the team."
Demichelis made 40 appearances for Malaga last season.