He was murdered alongside Chinese Chinese hostage Fan Jinghui.
The terror group's English-language Dabiq magazine featured graphic photos of what appeared to be the bloodied bodies of both men.
The bodies were pictured adjacent to photos of the blindfolded captives apparently taken just before their execution-style killings.
A stamp-like caption overlaid on the full-page photo read, “Executed after being abandoned by the kafir (disbeliever) nations and organisations.”
It was unclear how they were killed, but their heads were bloodied by apparent gunshot wounds.
The Norwegian prime minister's office said the photos “seem to show that the hostage Ole-Johan Grimsgaard-Ofstead was executed. We are still verifying it.”
It was the 12th edition of Isis's publication, one of many branches of the jihadist organisation's multilingual media machine.
The magazine's cover photo featured what appeared to be French aid workers at the scene of Friday's bomb and gun attacks in Paris that killed 129 people and were claimed by IS.
The caption read “Just Terror”.
“The Islamic State dispatched its brave knights to wage war in the homelands of the wicked crusaders, leaving Paris and its residents 'shocked and awed,'” Dabiq said.
In 2014, Isis declared a self-styled “caliphate” across territory in Iraq and
Syria where it imposes its extreme interpretation of Islamic law.
It has used its magazine and other media arms to publicise its gruesome murders, including the beheadings of American journalists James Foley and Steven Sotloff, Japanese journalist Kenji Goto, US aid worker Abdul-Rahman Kassig and others.
The Chinese and Norwegian hostages were last featured in the magazine's September edition, in which IS asked for an unspecified ransom for their release.
Neither that edition nor the one released on Wednesday gave details about where or when the men were captured, held or killed.
The Norwegian, 48, was once connected with a university in Trondheim but who appeared not to have been employed before his capture.
A university friend told Norwegian TV2 that he had been “totally obsessed with the war in Syria.”
In September, Grimsgaard-Ofstad's family said it was unable to pay the ransom asked by IS and appealed to his hostage-takers to release him.
The Norwegian government ruled out paying for his release, with Foreign Minister Borge Brende saying it was “out of the question for Norway to pay a ransom”.
Norwegian authorities said Grimsgaard-Ofstad was abducted January shortly after his arrival in Syria.
His last post on Facebook was on 24 January, when he wrote: “I am in Idlib, Syria. Going to Hama tomorrow. I finally made it.”