"When I won the FA Cup and the Community Shield, I told my family that it’s time to have a new challenge," Martinez said.
"He (manager Dean Smith) explained why he wants me here, the process that he wants from the club and also the playing style, and that’s why I decided to come here.
"Aston Villa gave the opportunity, I trust the process, the playing style and I truly believe that we can have a good season."
Following a decade-long spell at Arsenal that included a half-dozen loans, Martinez became the Gunners' first-choice 'keeper after the restart when Bernd Leno went down injured against Brighton on June 20.
Martinez started in the successful FA Cup final victory over Chelsea and the Community Shield win against Liverpool, and he was widely praised both for his shot-stopping skills and quality in distribution.
Leno was restored to the starting XI for Arsenal's 3-0 opening-day victory over Fulham as Martinez was omitted from the team sheet amid rumors of an impending move to Villa Park.
Martinez, who was also linked with Brighton, becomes Villa's third summer signing after Dean Smith's charges splashed a club-record fee for former Brentford forward Ollie Watkins and lured right-back Matty Cash from Nottingham Forest.
Villa, who secured Premier League safety on the final matchday of the 2019-20 campaign, kick off their season when they host Sheffield United on Sept. 21.