The 51-year-old takes over ahead of the two-match Test series against Pakistan later this month, the official said, adding that a formal announcement was expected shortly.
Arthur previously coached South Africa, Australia and Pakistan.
Details of the two-year contract were not immediately available, but three others are also due to join him in rebuilding the Sri Lankan coaching department, the source said.
The others are Grant Flower as batting coach, David Saker in charge of bowling and Shane McDermott handling fielding.
Hathurusingha and his assistants came under under fire after Sri Lanka's disappointing World Cup, where they finished in sixth-place.
Sri Lanka's then sports minister Harin Fernando had also complained about Hathurusingha's remuneration - $40 000 a month - saying it was too high.
"If we are winning only 35 percent of the games, no need to pay such high fees to coaches," Fernando said in August after putting Hathurusingha on notice to quit.
Hathurusingha remains officially employed with his contract valid for another year, but without any duties.
Fernando had said that there were international candidates to replace Hathurusingha who were asking for lower salaries of between $17 500 to $25 000 a month.