After launching a solo career, she was responsible for hits such as Escaping and Boy in the Moon in the late 1980s and early 1990s.
In 2021, she was inducted into the New Zealand Music Hall of Fame.
A cousin of fellow Kiwi musician Peter Urlich, Margaret Urlich is one of the most successful trans-Tasman musicians ever, selling more than 400,000 albums during her career.
She found fame in Australia for singing The Horses with Daryl Braithwaite.
She did not appear in the music video for The Horses and model Gillian Bailey lip-synched her backing vocals instead, with Urlich later saying she regretted not taking part.
"I was nicknamed Gilli Vanilli for a while," she told News Corp in 2016.
"I was recording an album in London when they did the video. I could have come back to do the video but I was doing my own thing by that stage. A lot of people know it's my singing, but they don't put two and two together that it's not me in the video.
"In retrospect it was probably a little bit silly because the song was so huge. But at the time I was young and a bit stupid, I did what I thought was right. But it was absolutely no disrespect to Daryl."
The Horses took four months to reach No. 1 in Australia in 1991, and eventually spent 12 weeks in the Top 10.
It has since become a cult classic in Australia and regularly features on TV shows and adverts.
She won an Australian ARIA music award in 1991 for Best Breakthrough Artist after becoming the first female solo artist to top the New Zealand charts.
Her song Escaping was a a number one in New Zealand and her first two albums, Safety in Numbers and Chameleon Dreams, made the top five in Australia.
Ulrich went on to release two more albums, The Deepest Blue (1995) and Second Nature (1999).
She also released a live album in 1994 and was part of the New Zealand cast of Jesus Christ Superstar in 1993.
She was diagnosed with cancer two years ago and had been living with her partner in New South Wales.
"It is with incredible sadness that we inform you that Margaret Urlich passed away peacefully on August 22 2022 at her home in the Southern Highlands of NSW, surrounded by her family after a courageous two-and-a-half-year battle with cancer," a family statement said.
"Margaret is a much-loved multi award-winning member of the Australian and New Zealand music industry who captured hearts around the world as a gifted singer/songwriter with a unique voice and sense of style.
"We thank you for respecting the privacy of her family and loved ones at this sad time."