Ms Norton, a Brit who grew up in South Africa, said the social group met once or twice a month and was open to anyone, but mainly new migrants to the area.
"I think we have just about every nationality you could have," she said.
Just four years ago, Hawke's Bay had a net loss of 1000 migrants each year.
Nationwide, net migration is also the highest since at least 1990.
More than 124,000 immigrants entered New Zealand in the year to March, while 56,450 emigrated, resulting in a net gain of 67,619 people - the highest net figure in at least 26 years.
These figures include New Zealanders returning after being away for more than a year.
Multicultural New Zealand executive director Tayo Agunlejika said immigrants created a diverse and dynamic New Zealand.
"It's a very positive thing - it gives you a vibrant society where not everyone is the same. It comes with its own challenges, but it's good for society," he said.
He said the most difficult factors for new immigrants were culture shock and isolation.
"They have to start fresh with social capital and for some of them there's a language barrier, too.
"Some of them don't get employed in an area related to their skills and experience but for most people it's the cultural shock."
However, he said many immigrants were still poorly treated because of their ethnicity - an area Mr Agunlejika was trying to improve.
"We still have the challenge of discrimination. We're trying to run a campaign to encourage people to realise it's okay to be different - that being different is positive and it makes a rich society.
"You don't need to be afraid if people are different to you. It's difficult to overcome but it's about educating people," he said.
In the past 12 months, 1862 more people moved from Australia to New Zealand than the other direction - a huge reversal from 2012, when almost 40,000 people a year were leaving.
Between May 1991 and September 2014, there has been a net loss of migrants across the Tasman.
Welcome group helps new arrivals
Lara Shah moved to Hawke's Bay with her 4-year-old son, Kala, about a year ago.
While living in Auckland, the 46-year-old visited the Bay for a short trip and ended up making the stay permanent.
"I thought I'd be returning to Auckland after the visit but I came, really liked it and ended up staying," Ms Shah said.
"I just felt like I would end up here - that it was just a matter of timing. I followed my intuitive feeling.
"We really love it and my little boy loves it - and him being happy is one of my top priorities."
Originally from Hawaii, Ms Shah is an author and does healing work for clients throughout the world.
She says the transition to the Bay has been smooth and she is a regular at the Newcomers' lunch group events.
"Everyone here is really nice and welcoming.
"The only thing that I've found a little bit difficult is it takes quite a long time to make friends and I've actually heard this from other foreigners, too.
So it's helpful that there's this group so you can meet up with other people."