The 28-year-old Argentine, who made 23 appearances last season and played in the Gunners’ FA Cup final win over Chelsea, has signed a four-year deal.
Villa manager Dean Smith said Martinez will be a “key player for our club for the long term”.
“It is rare to be able to buy a top-class goalkeeper who hasn’t yet reached their peak age,” he added.
“We know how highly Arsenal rated him and we watched his outstanding performances last season in a trophy-winning, top side.”
Martinez leaves Arsenal 10 years after joining as a youth team player in 2010.
Gunners manager Mikel Arteta decided Bernd Leno would be his first choice this season and the German started Arsenal’s Premier League opener on Saturday – a 3-0 victory at Fulham.
He is Villa’s third recruit of the summer after striker Ollie Watkins signed from Brentford for a club record fee and right-back Matty Cash arrived from Nottingham Forest.