The experienced Argentine international has penned a three-year contract in West London.
"I’m delighted to be at this football club," Martinez said upon his unveiling. "Coming to Chelsea, for me and my family, was an easy decision to make and I’m just over the moon - I can’t wait to get started.
"I want to be successful here. I'm someone who wants to win at everything I do, and I want to bring that here to this football club because it’s a football club that wins titles, so I think it’s a good match.
"I’m all passion, and I play with my heart. I will give 100 per cent every game, every training session to make the club, my teammates and the supporters proud."
Chelsea acted quickly to bring in Martinez after an error-strewn display from Robert Sanchez in their season-opening win at Fulham.
The 33-year-old was considered available for transfer by Villa after signing Japan goalkeeper Zion Suzuki from Parma.
Martinez made 256 appearances for Villa since joining from Arsenal in September 2020 and emerged as a significant figure at the club.
He started in the Europa League final last season as Villa beat Freiburg to win their first major trophy in 30 years.
A World Cup winner and two-time Copa America champion, Martinez has 67 Argentina caps to his name.
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