The First Minister addressed the Confederation of Norwegian Enterprise conference in Oslo on a visit to Scotland's sixth-largest trading partner.
In her message to Norwegian business leaders, Ms Sturgeon spoke of her regret that freedom of movement would end after Brexit but argued an independent Scotland could "achieve a true partnership" with the rest of the UK and other European nations.
"That will remain true regardless of Brexit, I hope, and whatever Scotland's future constitutional position.
"The Scottish Government is determined to work with the Norwegian Government and Norwegian businesses to strengthen those relationships."
Praising the country's "leadership on human rights, equality and ethical investment", Ms Sturgeon added: "Norway is a shining example of how small, northern European nations which are independent have been able to use their powers, not simply to improve the lives of their citizens at home but to play a constructive part on the world stage."
Turning to the issue of climate change, she said: "Both Scotland and Norway understand the importance and the urgency of moving to a net-zero emissions future."
Ms Sturgeon pointed out how the two nations had relied on the oil and gas industries but added: "We now need to make a just transition to a low-carbon and then a net-zero age."
She spoke of her support for the North Connect project that would lay 600km of cable between Scotland and Scandinavia to enable the transfer of surplus energy from renewable sources - such as Scottish wind farms or hydroelectric schemes - to where the power is needed.
"It would help both Scotland and Norway to reduce our carbon emissions while increasing our energy security and I very much hope we see it go ahead," she said.
Ms Sturgeon travelled to Norway by plane, although her officials say the carbon emissions of her flight will be offset.