The 31-year-old has signed an 18-month contract with the Premier League leaders with the option to extend for another year.
Jorginho had six months remaining on his Chelsea contract.
He joined the Blues from Napoli in the summer of 2018 and went on to feature 213 times for the club, winning the Europa League, Champions League, UEFA Super Cup and FIFA Club World Cup.
In a statement, Chelsea paid tribute to the Italy international, saying: "A leader on and off the pitch from the moment he arrived in west London from Napoli, Jorginho was coolness personified from the penalty spot with his trademark hop-skip technique.
"A friendly and funny guy off the pitch, Jorginho leaves Chelsea with 213 appearances to his name and four winners’ medals, none more precious than the 2021 Champions League success in which he played a major part. Good luck in the future, Jorgi!"
Arsenal turned their attention towards Jorginho after failing to conclude a deal for Brighton and Hove Albion midfielder Moises Caicedo.
"Jorginho is a midfield player who has intelligence, deep leadership skills and a huge amount of Premier League and international experience," said Arsenal boss Mikel Arteta.
"He has won in his career, but still has the hunger and huge willingness to contribute here.
"We are so pleased to sign Jorginho and welcome him and his family to the club."
Jorginho could make his debut for the North Londoners against Everton this weekend.
