Hjorter began his studies at Uppsala university in 1713, and was an astronomy student of professor Per Elvius.
After two years of studies he was forced to leave the university due to lack of financial resources and started working as private teacher in various noble families. He continued his studies in astronomy and mathematics on his own and calculated for example ephemerides for the Sun and the Moon. One of his employers, the family Jean Jaques de Geer, travelled to the Netherlands in 1723 and Hjorter accompanied, as a teacher for their son. In the following years Hjorter had the opportunity to study at several universities there, and in Utrecht he became assistant to professor Musschenbroek at the new Utrecht observatory. After his return to Sweden in 1727 he was forced to continue as a private teacher.
In 1732 Hjorter was employed by Count Axel Oxenstierna, a keen amateur astronomer, and was encouraged and supported by him to continue at Uppsala university. After his studies in the Netherlands he now had a solid education in astronomy and mathematics, but still no formal exam. Several professors at Uppsala university realized his education and abilities, and since the professor in astronomy, the later famous Anders Celsius was away on his long journey abroad, and as the professor in mathematics found the additional lectures in astronomy too strenuous, Hjorter was employed as lecturer.
Hjorter was a very competent and popular lecturer, and when Celsius returned to his professorship in 1737 he found that astronomy in Uppsala had prospered during his absence with many talented students. Hjorter now became the assistant of Celsius, and they continued a close fellowship up until Celsius' death. Hjorter's astronomical work is therefore closely related to Celsius own work, and can be found in many papers by Celsius. He observed carefully the total solar eclipse in 1733 and was the first in Europe to professionally observe the great comet of 1744. He also carried out many latitude measurements in various places for the General map of Sweden, and calculated many almanacs. His auroral research, together with Celsius, became later world famous.
After the death of Celsius in 1744, he was not appointed professor in astronomy due to his lack of a formal university exam. Hjorter was instead appointed to a new observational professorship at Uppsala university: "Observator Regius" - "Royal Observer", established fully in 1747.
Hjorter became a member of the Celsius family through his marriage to Anders Celsius sister, and the very large and valuable book collection accumulated by the Celsius family for several generations was inherited by Hjorter. He donated the collection, toghether with instruments and a large sum of money to the Uppsala observatory in 1747.