Martinez is expected to complete a £20m to Dean Smith’s side in the coming days in search of regular first team football.
The 28-year-old Argentine is currently Arsenal’s longest serving player, having joined the club from Indepediente in 2010 but he has played second fiddle for much of his time in North London and has spent time on loan at Oxford United, Sheffield Wednesday, Rotherham, Wolverhampton Wanderers, Getafe and Reading.
Martinez impressed when he got a decent run of games under his belt towards the end of the 2019/2020 season after first choice Bernd Leno got injured.
Martinez made nine Premier League appearances last season and was in goal when Arsenal beat Chelsea and Liverpool in the FA Cup final and Community Shield respectively.
Saying goodbye to Arsenal in an Instagram video on Tuesday, the 28-year-old said: "Thank you Arsenal. 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.
"They all understood at Arsenal and they support me for my decision. The Arsenal fanbase were always there for me, I felt their love.
"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."
