Sri Lanka Cricket (SLC) secretary Mohan de Silva said the country had been without a proper coach since the early World Cup exit.
Arthur, who has previously coached Pakistan, Australia and South Africa, will accompany Sri Lanka on their tour to Pakistan this month.
The board did not talk about about the terms of their two-300 and sixty five days contracts, but doubtlessly the most contemporary appointments successfully end head coach Chandika Hathurusingha's controversial role with the crew. "They have pace and with little bit more experience they will be great for Pakistan in the future".
Arthur will likely be assisted by Zimbabwean Grant Flower, who will likely be Sri Lanka's batting coach, in addition to Australians David Saker and Shane McDermott, who will likely be bowling and fielding coaches respectively.
The board would not say what they plan to do with Hathurusingha who has refused to step down despite being sidelined since August.
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Arthur was recently released from his short-term Twenty20 contract with New Zealand side Central Districts.
Arthur arrives following three years with Pakistan, who he led to the 2017 Champions Trophy title in addition to primary within the Take a look at and T20 rankings.
He left that role after they had also failed to reach the semifinals of the World Cup, but said after accepting the Sri Lanka job: "It had been three very good years with Pakistan and I needed some time".
Arthur's first assignment will see him return to Pakistan for a two-match Test series starting on 11 December.
"The Head Coach has been charged with six counts including failing to prepare the Sri Lanka team physically and mentally for tours; failing to build confidence of players in need to [sic] support; for creating disharmony and failure to build team spirit; failure to adhere to the ICC's Code of Conduct; insubordination; and acting in a manner which is totally unbecoming of a National Head Coach", the report in the Sri Lankan newspaper revealed.