"I can only be grateful to Barca for their respect and special appreciation, and I would like to thank them for giving me three years at a club as great as Barca," Marca quotes Villa as saying.
"I have no complaints about Barcelona and they made it easy for me to move to Atletico because they knew I wanted to play here. I hope I can be just as happy at Atleti as I was at Barca.
"This is a winning team which has won lots of titles in recent years. I've come to help the club improve a little. I've spoken to coach Simeone and his trust was one of the keys to me coming here. I can't wait to start taking orders from him and repay that trust."
Villa spend three years at Barcelona, having joined them from Valencia in 2010.