Godin, who helped his country finish fourth at this summer's World Cup, joined Villarreal in 2007 from Nacional in his homeland and established himself as a regular for the Yellow Submarine.
And he is desperate to build on his promise after joining the ranks of the reigning Europa League champions.
"I want to do well at this club and give titles to the fans. I'm at one of the biggest clubs in Spain and Europe. This opportunity is a challenge for me," he said.
"I bring many things and want to help a great group here. Winning the Europa League demonstrated that they are a great team, it was not won by chance.
"I hope I can help Atletico to continue winning titles.
"We know that the struggle in the league will be very hard; the goal is to be in the Champions League."
"Diego told me that Atletico is a great team, you demand a lot and want to win every game," Godin added. "He stressed that if you give your all on the field and strive in every game, fans will recognise it."