Jebsen was born in a small town near Oslo and majored in physics at the University of Oslo. After graduate study in Berlin, where he worked on X-rays, he returned to Norway, worked on a master's degree in Oslo, and contemplated extending it to a Ph. D. At this time, Albert Einstein's then new theory of gravitation, the general theory of relativity, was the subject of much enthusiasm among the graduate students, although the faculty was more cautious, apparently feeling out of their depth. Jebsen's thesis was on electrodynamics within Einstein's special theory and was referred to the closest thing they could find as an "outside expert" on relativity, Carl Wilhelm Oseen at Uppsala University.
Oseen, apparently sensing Jebsen's talent, pointed out some errors and asked Jebsen to resubmit his work after making improvements. This became Jebsen's master thesis. Furthermore, he was in 1919 invited to Uppsala by Oseen and it was here he started his work on general relativity and in particular his generalization of the Schwarzschild solution. The result was written up for publication in the spring of 1920. Unfortunately, Jebsen had been diagnosed with an aggressive case of the then chronic and fatal affliction of tuberculosis. Seeking to prolong his life, he moved to Italy, where he died in 1922.
Oseen apparently sought to helped finance publication of the (German language) paper by the impoverished Jebsen, mentioned the theorem in his own 1921 English language review, and kept up a correspondence with the younger man until Jebsen's death. Despite Oseen's efforts, it seems that Jebsen's work sank like a stone and when the famous mathematician G. D. Birkhoff rediscovered and published the theorem in 1923 (without knowing of Jebsen's prior work), it was named for Birkhoff.