The Spain international is reportedly on the brink of signing for new MLS franchise New York City FC, who will join the league next season.
Villa scored 13 goals in 36 La Liga appearances for Atleti last season, as Diego Simeone's men celebrated a first league triumph since 1996, while they were losing finalists in the UEFA Champions League to city rivals Real Madrid.
The former Barcelona forward took the time to thank the club for a "great experience", and is relishing a new challenge outside of Spain.
"(I am) excited with this important project, for me, and for my family, personally and professionally," he told Atleti's official website.
"And I am very excited to start a new challenge, which is what I have tried along my whole career, and I think this is a really important one for my life in general.
"It has been a great experience, not only around sport matters, that you have all seen, but further than that. Personally I found a great family, inside the locker room, the communion with the supporters and the club.
"That has helped me a lot, and honestly, they have make me feel really happy. I will remember this year all my life."
Villa revealed that owner Enrique Cerezo and chief executive Miguel Angel Gil Marin wanted him to remain at Vicente Calderon, but the 32-year-old could not resist the chance of a new experience.
"(I want to) thank all the Atletico aficionados, everyone from the club who wanted me to stay here," he added. "Especially 'Cholo' (Simeone) and his staff, who transmitted that they wish me to stay in the team.
"And obviously I thank Enrique and Miguel Angel, who as well offered me to stay. But as I said before, this is something you can't refuse, a great project that I must accept."
