The 33-year-old joins on a three-year contract, bringing the curtain down on a five-year spell at Aston Villa that included 256 appearances and a Europa League triumph last season.
Martinez, who won the World Cup with Argentina in 2022 and previously came through the ranks at Arsenal, described the move as a straightforward decision.
"I'm delighted to be at this football club. 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," he said.
"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."
Manager Xabi Alonso wasted no time handing Martinez his debut, starting him against Brighton on the day the deal was completed.
"We are very happy with Emi and we are delighted to have him here at Chelsea," Alonso said before kick-off. "To have such a goalkeeper of this stature, of this personality, it's very good for us. I think that he will bring lots of qualities, and I'm sure that he can have a straight impact, and that's why we decided that he's ready to play straightaway."
The move continues an unusually close trading relationship between the two clubs, with Martinez becoming the eighth player to switch between Chelsea and Villa in the past four years.
His arrival at Stamford Bridge follows growing scrutiny of Chelsea's existing goalkeeping options after a shaky start to the season, and gives Alonso an experienced, vocal presence between the posts as the club looks to build momentum through the remainder of the transfer window and beyond.