The experienced attacker has thanked the Liga champions for his time at the club and is looking forward to wearing the Atletico Madrid jersey
The Spain international, 31, will leave Barca for Atletico Madrid in a deal worth €5.1 million [£4.3m], with €3m [£2.6m] being paid if Villa remains an Atletico player during the 2014-15 and 2015-16 campaigns.
Bought for €40m [£34m] from Valencia in 2010, the striker has hailed the Blaugrana's decision to allow him to switch clubs on the cheap.
"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," Villa was quoted as saying by Marca.
"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 [Diego] 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 will be officially unveiled at Atletico on July 15.