Ex-bowler Rumesh Ratnayake was named Sri Lanka's interim coach in August.
That came after former head coach Chandika Hathurusingha, was criticised for Sri Lanka's exit at the group stage of the 50-over World Cup in England.
Arthur had been in charge of Pakistan for three years and led them to the 2017 Champions Trophy title.
But Pakistan decide not to renew his contract in August, after the country failed to reach the semi-finals of this summer's World Cup.
Zimbabwean Grant Flower will join Arthur's support staff as batting coach, while Australians David Saker and Shane McDermott will be bowling and fielding coach respectively.
Arthur said: "It had been three very good years with Pakistan and I needed a little bit of time away. The Sri Lankan job became available and I started discussions.
"I looked at the talent that's available and that's the key motivating factor - to help these young players fulfil their potential."
Arthur's first assignment will see him return to Pakistan for a two-match Test series starting on 11 December.