"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.
Since former Argentina captain Simeone took over at Atletico in December 2011, the club have won the Europa League and the European Super Cup in 2012.
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."
Villa bore no grudges against his former employers, Barcelona.
"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."
No date has been fixed yet for his official presentation.