Frebel, 34, who heads Noma's research and development team, is launching Inua on 29 June, with the financial backing of Redzepi and Japan's Kadokawa Corporation.
“When I was here with Noma, I felt this strong connection with Japan. I was drawn to the landscape, the culture and the ingredients,” Frebel said in a press release announcing the launch on Thursday.
“When we left, I felt a sense of not being finished with my time in Japan. Fulfilling my dream, I'm excited to be back in Tokyo, one of the world's greatest food cities, to open and share Inua.
Redzepi told Denmark's Berlingske that Inua "will not be a Noma restaurant".
"But it will be the first super ambitious overseas restaurant with Nordic roots," he added. "It's Thomas who makes all the decisions, and it's him who came up with the name and approved the design."
But Frebel said he would bring Noma's food philosophy with him.
“After ten years, there is now a little bit of me in Noma and a lot of Noma in me," he told Berlingske.
In the press release he said the restaurant, which has been designed by the Danish interior company OEO Studio, aimed to combine “Japanese ingredients and a Nordic sensibility”.
Redzepi said he did not feel that Frebel's departure from Noma after 10 years was a farewell.
"I can directly relate so much of Noma's success to his work ethic and spirit. He's the most talented and hardworking chef I've ever had the pleasure of knowing," he said. "This wasn't so much a goodbye as a continuation of our shared creativity.”