Next will acquire a further 21% stake in Reiss, upping its holding from 51% to 72%. The Reiss family's holding will increase to 22%, with the other 6% held by Reiss management.
Together, Next and Reiss will pay £128 million for just over a third of the business.
Next initially bought a 25% stake in Reiss from Warburg Pincus in 2021, at the time valuing the brand at around £200 million.
Next chief executive Simon Wolfson said: "Reiss has performed exceptionally well since we first invested in March 2021. This success has been driven by the strength of its brand, first class management and the benefits of Total Platform; we look forward to continuing to develop the business with Christos and the Reiss team.
“Warburg Pincus has been an excellent partner throughout the term of our investment and we have enjoyed working with them during the last two years."
Christos Angelides, Reiss chief executive, suggested the deal may allow for further expansion of the brand.
“We are appreciative of the excellent partnership with Warburg Pincus over the past seven years - their expertise has been instrumental to our sustained development and they have been a strong and trusted partner,” he said.
“We look forward to continuing to focus on creating authentic and timeless collections for our customers and over the next few months we will be launching a number of new initiatives that will both expand the breadth and choice of our collections worldwide.”
Next has reported booming sales in recent months, upping its profit guidance twice as it said customers were spending their pay rises on new clothes.