Muralitharan, who holds the records for the most wickets in Tests and one-day internationals, is honouring a commitment made to former New Zealand captain Stephen Fleming.
"I've always enjoyed my time in New Zealand and it is a fantastic country to tour and to play cricket in," he said in a statement.
Wellington chief executive Gavin Larsen who announced the deal described it as a "tremendous boost for Wellington to secure the services of one of the greatest international cricketers of all time.
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His services are desperately needed by Wellington who have never finished better than fourth out of six teams in New Zealand's Twenty20 domestic competition.
The 39-year-old Muralitharan, who retired from international cricket after Sri Lanka lost the World Cup final to India last month, struck up a friendship with Fleming when they were involved with the Chennai Super Kings in the Indian Premier League.
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Fleming has coached Chennai for the past two seasons while the auction system f