"I have spoken to Simeone and one of the keys to coming here was his confidence," Villa told reporters after passing a medical test with Atletico.
"I am really looking forward to working for him, and to being able to return that in every training session and every game."
Spain's all-time leading scorer agreed a move to Atletico on Monday for a fee that could rise to 5.1 million euros if he stays at the Calderon for the next three seasons.
The 31-year-old's future with the La Liga champions looked uncertain after they signed young Brazil forward Neymar in May, and he was linked with a number of Europe's top clubs before Atletico stepped in.
Last May, they beat Real Madrid to win the King's Cup final and finished third in La Liga to earn a place in the Champions League group stages for next season.
"Atletico are a team of winners. They have been competing on all fronts in recent years," said Villa, who arrives as a replacement for the departed Radamel Falcao.
"I am coming to be just one more in the squad and to help a settled team improve and to become even more competitive. I hope I can do my part."
"I have no complaints," he said. "They have helped me from the very first day because they knew I wanted to come and play here. I hope I can be as happy here as I was there."
