New Zealand captain Brendon McCullum has claimed that he and his teammates are having the "greatest time of our lives" following their dramatic win over South Africa in the Cricket World Cup semi-finals.

The co-hosts made it through to their first ever final on Tuesday thanks to a nervy four-wicket victory in Auckland.

The rain-affected match came down to the final over, but it was New Zealand who advanced when Grant Elliott hit a giant six for the win.

"It's the greatest time of our lives as players," McCullum is quoted as saying by Sky Sports News. "It's an incredible ride, the crowd has supported this team and the brand of cricket we have played. Hopefully they're dreaming like we are.

"It would be nice to win it. Both teams in the other semi-final are quality teams and we know if we play the way we can we have a chance.

"It was a great advert for cricket. Everyone that was here will remember it for the rest of their lives. We have given ourselves a chance of World Cup glory and I'm proud of our efforts."

New Zealand will face either Australia or holders India in the final.