Record-breaking New Zealand boss Steve Hansen has hailed Ireland's Joe Schmidt as one of the world's best coaches.

All Blacks head coach Hansen praised his fellow Kiwi Schmidt in the wake of Ireland's 40-29 victory over New Zealand at Chicago's Soldier Field on Saturday.

Ireland ended their 111-year wait for a victory over New Zealand in the US, cutting short the back-to-back world champions' record winning streak at 18 matches.

Hansen also admitted the New Zealand Rugby Union (NZRU) had worked hard to prise Schmidt away from Ireland and back into their Super Rugby coaching set-up.

"He's probably one of the best coaches around," said Hansen of Ireland boss Schmidt.

"He's meticulous in his work ethic, a good analyst of the game and that's why Ireland want to keep him and why New Zealand wanted to bring him home."

Schmidt only signed his new Ireland contract two weeks ago, committing his future to the IRFU until after the 2019 World Cup.

"They're having a great year, they've knocked over South Africa and they've knocked us over. So he'll be feeling pretty pleased with himself and so he should."

The 51-year-old had seriously considered taking a coaching job with either the Highlanders or the Chiefs, but eventually opted to remain in Dublin.

Family concerns and the desire to lead Ireland past the quarter-finals of a World Cup for the first time tipped the balance in the end however.

Schmidt has already assured his place in Irish folklore courtesy of Saturday's victory, whatever happens next, but New Zealand coach Hansen expects his countryman to continue to guide Ireland on an upward curve.

Hansen believes Schmidt can rightly be viewed among the sport's shrewdest minds, after adding the maiden All Blacks scalp to Ireland's first win over the Springboks on South African soil in June.

"It's good for Joe, and Joe's a really good man, I've got a lot of time for him as all our coaching staff has; he's a top bloke," said Hansen of Schmidt.

"He's working hard and trying to do something with Ireland and he's having some success.

"They're having a great year, they've knocked over South Africa and they've knocked us over. So he'll be feeling pretty pleased with himself and so he should."