The Argentine goalkeeper, 28, has committed to join Villa after the clubs agreed on a deal worth £16m bid plus add ons.
In a message captioned 'Thank you Arsenal', Martinez said in an Instagram video: "For me, I could not be happier to leave through the front door with the Arsenal fanbase supporting me and the club supporting me.
"I had 11 years at the club, and even if it was a hard road for me, and I suffered through my time at Arsenal, today I am happy and I tried to show young goalies how work pays off.
"When you work hard, you are not going to be happy the whole time, you are going to have frustration, bad times in life.
"Even when Bernd got injured this season, I received loads of messages like "we trust in you," "you are our goalie". That made me confident, made me win games and made me the keeper I am today.
"They understood my story and they love the way I worked in the club. I am so glad to be part of the Arsenal family for 11 years."