The 31-year-old was unveiled at the Vicente Calderon after completing a cut-price 2.1million euro move from Barcelona. The fee paid to the Spanish champions will rise to 5.1m euros if Villa sees out the entirety of a three-year deal.
The Spain international started less than half of Barca's league games last season to put a host of European clubs on high alert, with Tottenham among the Premier League clubs closely linked with a move for the former Valencia forward.
But when Atletico approached him in early July, he knew his future lay with the capital club.
He told reporters: "We had a move to the Premier in mind but then Atleti appeared and within three days all my personal terms had been agreed.
"From a career point of view, they weren't lacking anything. They finished third and will play in the Champions League. They beat Real Madrid to win the Copa del Rey.
"Starting from today, the best club in the world for me is Atletico Madrid."
Villa's challenge will be replacing the goal threat that disappeared to Monaco when Colombian hitman Radamel Falcao made a surprise switch to the principality last month.
Falcao hit 28 league goals in the 2012-13 season and 52 in just two years with Atleti, but Villa hopes his own goal record will stand up to scrutiny in southern Madrid.
The Asturian has scored 282 career goals for Sporting Gijon, Real Zaragoza, Valencia and Barcelona, with his 91-cap adventure with Spain yielding 56 goals to date.
"I have to talk to the coach (Diego Simeone) about playing in a number nine role, where Falcao played," Villa added.
"But I am simply at his disposal and will play wherever he wants. (Falcao) was loved here but hopefully I can make sure his absence isn't felt."
Briefly touching on his reasons for leaving Barcelona after three successful seasons, he added: "I left Barca because I wasn't playing, not because the World Cup was on the horizon. I love this game and I wanted to play it."