The Colombia international had helped the team finish third in the La Liga table last season and qualify for the Champions League this year. But the 27-year-old has been lured away to Monaco in Ligue 1 for next season.
Villa was weighing up a move to England when his mind was swayed by Atletico, as he informed a press conference at his unveiling on Monday.
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.
However, Villa's unveiling in front of adoring supporters at the Vicente Calderon Stadium did not quite go according to plan.
While the Spain striker showed his skills during his presentation, some fans encroached on to the pitch to greet the new arrival with a personal touch.
In scenes reminiscent of music fans greeting The Beatles during the 1960s, Villa appeared to have become the subject of some over-zealous supporters.
And as security guards wrestled the initial invaders to the ground, more supporters ran on to the pitch and Villa was whisked away down the players' tunnel.
But now the 28-year-old has further championships on his mind with the Viola, as Alex Moretto of Goal.com reported.
My dream is to be able to win a title here in Italy.
Fiorentina made it clear they have ambitions in the league and want to take a step forward. They came fourth last year and want to be even more competitive in Serie A and also in Europe next season.
I will not guarantee a certain number of goals. What matters is to score those needed for the team to get as many wins as possible.
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