Norway's success means that all five Nordic countries will now be competing in the final on May 10.
"Now I'm so happy that I can't find the words," Thorbjørnsen told VG after the results were announced. "I am so very happy and very satisfied with my own performance. The hard work has paid off. It can be described as an extreme bliss."
Torbjörn Ek, a Eurovision expert for Sweden's Aftonbladet newspaper, who had previously criticised Thorbjørnsen for showing nerves in his performances, told the channel that in the semifinal it had all come together.
"It's the best he's done down here," he said. "He…seems nervous in the first minute. But his singing was cracking! And eventually he will get his nerves under control."
Austria's controversial entry, bearded drag queen Conchita Wurst, also made the final, with "Rise Like a Phoenix", a power ballad that would not be out of place in a James Bond film, as did entries from Poland, Belarus, Romania, Malta, Greece, Switzerland, Slovenia and Finland.
Wurst, the drag persona of Austrian singer Tom Neuwirth, triggered a petition in Belarus calling for the state broadcaster to edit her out of the television footage to avoid turning Eurovision into "a hotbed of sodomy".