Mr Finn told the Rotorua Daily Post the couple would be retiring.
"One gets older and nothing lasts forever," said Mr Finn. "Max fashions wanted our site and approached us, and we've struck a deal."
The Finns have reached an agreement with the landlord to give up their lease, effective in four weeks, with Max taking over the site and beginning a major refit.
Mr Finn said he was pleased that a national brand was taking over the location.
"[It's] positive for Rotorua, and hopefully it will attract others."
Ms Hunt, the council's lead on inner city revitalisation, said Max's coming was fantastic news.
"Finns Fashions has been a stalwart in our fashion scene here," she said. "But the arrival of one of the bigger players in the market is signaling a turnaround for our city. It's a big win."
Ms Hunt said the move was significant, and she believed other high street brands would follow.
She said Max had specifically wanted the site because of its existing boutique offering, with several other fashion and art stores nearby.
Mike Steiner, spokesman for Rotorua's Inner City Focus Group, said it was significant that a multinational was coming to Rotorua at the higher end of the market.
"Three or four years ago we would not have been able to encourage that type of national retailing store to even consider coming to Rotorua," he said.
"They have obviously done their due diligence, and they feel it's a very viable proposition to open here, which might encourage other retail businesses as well."
But it was sad to see an iconic retail business like Finns Fashions closing, and the community would be sorry to no longer see it in the retail mix, he said.
Mr Finn said the couple had enjoyed a great life of fashion retailing.
"But we've got grandkids and all sorts of other little projects we want to focus on, so it gives us that opportunity to do other things."
The Finns are long-time Rotorua residents and plan to stay.
"I've lived here all my life," said Mr Finn. "We're still living in the same street I was brought up in. We love Rotorua. It's a great town."