RNZ reports the team won 20-3 over the Lions at Westpac Stadium at the weekend, the first time they had won the competition in 21 seasons.
The parade left Parliament at midday, where Prime Minister John Key turned out for a photo with the team.
Fans are lining the streets to see the players parade down Lambton Quay and Willis St, with victory speeches to be held when the parade ends at Civic Square.
