"Russel has informed his decision to team manager Michael Tissera in Jamaica and it has now been officially conveyed to the cricket board," SLC spokesman Samantha Algama told AFP.
Arnold will, however, continue to play domestic cricket, Algama added.
Sri Lanka, who defeated New Zealand in Tuesday's semi-final, will meet the winner between Australia and South Africa in Saturday's final in Barbados.
Arnold, 33, made his Test debut in Colombo against Pakistan in 1997 and enjoyed a permanent position in the Sri Lankan side between 1999 and 2003.
Temporary loss of form forced him on the sidelines over the past two years before the selectors brought him back for the World Cup.
Arnold played 44 Tests, scoring 1,821 runs with three centuries.
The World Cup final will be his 180th one-dayer. He has made 3,949 one-day runs with one hundred.