Arthur will replace Dave Houghton, who left the club at the end of the 2021 season.
It is said that Arthur will link up with the Derbyshire squad after Sri Lanka’s two-Test series against West Indies which begins on Sunday (21).
Reports add that Arthur tendered his resignation to Sri Lanka Cricket yesterday (16).
Tweeting, Arthur has also said, "Sad that it is the end of the road with SL after the WI test series!I have loved every minute of coaching this great country!To the players and people of SL a big thank you! I know SL cricket is in a better place now than when I started!."
Arthur, who is currently the head coach of the men's national team in Sri Lanka, has had coaching roles with Australia, South Africa and Pakistan.