Once Brexit happened, the UK would not make life any more difficult for Kiwis, he said.
"On the contrary, we love Kiwis coming to our country and it makes a huge difference to our economy that we have people with talent and ambition who want to come, even if it's only for a short time."
He wanted the post-Brexit regime for ancestry and working visas to be "at least as attractive as the current regime", he said.
Johnson reiterated that New Zealand would be "at or near the front of the queue" for a free trade deal once the UK formally left the EU, likely to be in two years' time.
Asked how he would appease British farmers who were wary about such a deal, Johnson said "no one is going to be any worse off".
"We already are the proud and grateful recipients of a lot of New Zealand sheepmeat and indeed butter. I think my grandmother would buy absolutely nothing else but Anchor butter, I want you to know."
He dismissed a suggestion that infighting within his Conservative Party could undermine any progress towards a free trade deal in the two years before Brexit took place. Any conflict within the party had "completely passed me by", he said, and he had heard no news of infighting while on his travels.
He admitted that the recent general election "did not evolve entirely in the way that the Government had hoped or wanted", while adding that "the Labour Party did not win" and the Conservative government was "getting on with the business of governing".
Johnson was greeted by a shout of "Boris for PM" at a ceremony in Wellington yesterday, and was asked today about the prospects of taking over Theresa May as Prime Minister.
"I don't know whether you were as eagle-eyed as I was at that wonderful ceremony yesterday, but I also spotted a protestor who took a diametrically opposite view."
There was no public appetite in Britain for "any more political kerfuffle", he added.
In his opening remarks, Johnson praised the closeness of the British and New Zealand governments, saying there was a "total failure to disagree on any point of substance" on trade, security or other issues.
"These are two countries which really do think on the same lines on so many views that matter to our people and to our electorates."
Security issues were on the agenda during today's talks, and Brownlee said the two countries were united in their condemnation of North Korean "provocations".
"I reaffirmed to Foreign Secretary Johnson that New Zealand will continue to support international efforts to bring security to the region."
Brownlee expressed sympathy to his British counterpart over the recent series of terror attacks in the UK, and said New Zealand was committed to the global coalition to defeat the Islamic State.
The Foreign Minister also referred to the recent Lions tour of New Zealand, saying the warmth between the two countries was "very much on display", while noting that the tied series left both sides "somewhat perplexed".