The purchase price represented a multiple of 8.8 times pro forma cash profit in the 2015 financial year, FlexiGroup said.
F&P Finance, whose products include Q Card and Farmers Finance, has receivables of $662 million, more than 12,000 partnerships and 43,000 active card holders, according to FlexiGroup.
"Fisher & Paykel Finance is a very high quality asset that FlexiGroup worked hard to secure because it compliments and offers synergy to FlexiGroup's existing card business," said acting FlexiGroup chief executive David Stevens.
He said it was a "transformational deal" for FlexiGroup.
"Fisher & Paykel Finance will significantly enhance the scale of FlexiGroup's NZ operations, provide access to new industry channels both in NZ and Australia, and opportunities for customer growth."
F&P Finance is owned by whiteware manufacturer Fisher & Paykel Appliances, which was acquired by Chinese home goods maker Haier in 2012.
The finance business, founded in 1973, was never central to the Qingdao-based firm's aims.
Haier made the acquisition largely to secure a more upmarket whiteware brand for its portfolio, as well as to gain access to the New Zealand company's research and development capabilities.
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Fisher & Paykel Appliances announced in May that it had appointed investment bank First NZ Capital to "assess potential options" for the future of its finance arm "in response to recent market interest".
At that time chairman Keith Turner said interest from potential buyers had been strong.
"Whilst [the company] is happy to continue to own FPF and support its ongoing development, it is very possible a change in ownership may be a better option," Turner said.
F&P Finance's other businesses are Consumer Insurance Services, which provides insurance and product protection policies to retailers and consumers, and Equipment Finance.
In April Fisher & Paykel Appliances reported a full-year loss of $12.6 million for the 2014 calendar year, an improvement on the $31 million loss it reported a year earlier.