Over 100 backers helped the fine-dining restaurant hit its goal just four days after the launch of its Kickstarter page.
Norse, which is listed in the Michelin Guide for Great Britain and Ireland 2017, currently runs as an evening pop-up in a Harrogate café.
The team will use the funding to move to a 40-cover site in Harrogate, with a larger kitchen, where the restaurant will be able to serve lunch for the first time.
Head chef Simon Jewitt will be a partner in the new venture, which could open as early as April this year.
The Kickstarter page will continue to accept pledges until 7 March.
“We owe a huge thanks to everyone that has backed and shared the campaign in the first four days,” says Norse owner Paul Rawlinson.
“We still have 25 days with the project live so it'd be a shame to stop now when we could achieve more.”
Norse launched in 2014 and received a glowing review from Observer food critic Jay Rayner just six months after opening.
Its menu includes scallop, apple, mushroom and bergamot; lamb with parsley root and seaweed; and clementine with chocolate and pine.
The restaurant is also recommended in the Waitrose Good Food Guide 2017.