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.
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