The 31-year-old says he is looking forward to helping his new club continue to grow following his summer move from Barcelona
The Rojiblancos have enjoyed a wave of success under Diego Simeone, securing the 2012 Europa League crown and the 2013 Copa del Rey.
And Villa, who is set to seal a move to the Vicente Calderon from Barcelona, wants the club to grow.
"It's a major challenge. Being here, coming to a great club and a group of winners," he told reporters. "I'll try to do my bit and give everything to make the club bigger so this group can keep delivering titles."
The 31-year-old went on to cite Simeone as one of the major reasons behind his move to the Spanish capital.
"I think he's just like he was as a player as a coach. With a lot of character, heart and football ideas that speak for themselves."
Finally, the former Valencia man said he is looking forward to playing at the Calderon.
"The Calderon is a pitch where every player wants to come to play. It's one of the stadia you mark on the calendar with joy as a visitor," he added. "I cannot wait. I'm looking forward to checking it out, to enjoy this area and these fantastic fans."