The 64-year-old will begin his new assignment later this month and join the team in New Zealand where, starting December 15, Sri Lanka are scheduled to play two Tests, three one-day internationals and one Twenty20.
They will later play two Tests in Australia from January 24.
"I am sure he will be able to help the team moving forward, with his expertise in the area of fielding which is a vital component of the game."
De Silva said Rixon will work with the national team until the end of the 2019 World Cup.
Sri Lanka have been struggling for form recently, losing the home ODI and Test series to England.
They have also been hit by crisis off the field.
The country recently sought help from neighbouring India to draft laws to combat cheating in the game.
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