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.
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"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," Villa observed. "With a lot of character, heart and football ideas that speak for themselves.
"The Vicente Calderon is a pitch where every player wants to come to play," he added. "It's one of the stadia you mark on the calendar with joy as a visitor.
"I cannot wait. I'm looking forward to checking it out, to enjoy this area and these fantastic fans."