The 31-year-old, who joined Chelsea from Napoli in 2014, is into the final six months of his contract at Stamford Bridge.
He will now have a medical before signing an 18-month contract with the option of a further year.
The Gunners turned their attentions to Jorginho after having two bids rejected by Brighton for Moises Caicedo.
Brighton say Caicedo is not for sale and it looks increasingly likely the Ecuador midfielder will remain at the club after the 11pm deadline.
Arsenal winger Marquinhos joins Norwich on loan
Jorginho is set to become Arsenal's third signing of the January window, the club having previously bought Poland defender Jakub Kiwior from Spezia for 20m euros (£17.6m) and Belgium striker Leandro Trossard, who moved from Brighton for £21m.
Mikel Arteta's side are five points clear at the top of the Premier League with a game in hand on the sides immediately below them.
Jorginho has scored 29 goals in 213 appearances for Chelsea, winning the Champions League, Europa League, Uefa Super Cup and Fifa Club World Cup during his time at at the club.
The midfielder was born in Brazil but moved to Italy at the age of 15 and opted to play for the Azzurri at international level.
He has 46 international caps and was part of the Italy side that beat England to win Euro 2020 at Wembley in July 2021.
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