Ørsted was born in Rudkøbing. As a young boy Ørsted developed his interest in science while working for his Father, who owned a pharmacy. He and his brother Anders received most of their early education through self-study at home, going to Copenhagen in 1793 to take entrance exams for the University of Copenhagen, where both brothers excelled academically. By 1796 Ørsted had been awarded honors for his papers in both aesthetics and physics. He earned his doctorate in 1799 for a dissertation based on the works of Kant entitled "The Architectonics of Natural Metaphysics".

In 1800, Alessandro Volta invented a galvanic battery inspiring Ørsted to think about the nature of electricity and to conduct his first electrical experiments. Between 1800 and 1803, he visited Germany, France and Holland for lectures. Ørsted welcomed william Christopher Zeise to his family home in autumn 1806; taking the then young Chemist (and fellow son of a pharmacist) under his care and giving him encouragement while offering him a position as his lecturing assistant. In 1812 he again visited Germany and France after publishing a manual called Videnskaben om Naturens Almindelige Love and Første Indledning til den Almindelige Naturlære (1811). In Berlin he wrote his famous essay on the identity of chemical and electrical forces in which he first stated the connection existing between magnetism and electricity. Then, in Paris he translated that essay into Latin with Marcel de Serres.

In 1801 Ørsted received a travel scholarship and public grant which enabled him to spend three years travelling across Europe. In Germany he met Johann Wilhelm Ritter, a Physicist who believed there was a connection between electricity and magnetism. This made sense to Ørsted since he believed in Kantian ideas about the unity of nature and that deep relationships existed between natural phenomena.

Their conversations drew Ørsted into the study of physics. He became a professor at the University of Copenhagen in 1806 and continued his research with electric currents and acoustics. Under his guidance the University developed a comprehensive physics and chemistry program and established new laboratories.

It is sometimes claimed that Italian Gian Domenico Romagnosi was the first person who found a relationship between electricity and magnetism, about two decades before Ørsted's 1820 discovery of electromagnetism. Romagnosi's experiments showed that an electric current from a voltaic pile could deflect a magnetic needle. His researches were published in two Italian newspapers and were largely overlooked by the scientific community.

In 1822, he was elected a foreign member of the Royal Swedish Academy of Sciences and in 1849 a Foreign Honorary Member of the American Academy of Arts and Sciences. .

In 1824, Ørsted founded Selskabet for Naturlærens Udbredelse (SNU), a society to disseminate knowledge of the natural sciences. He was also the founder of predecessor organizations which eventually became the Danish Meteorological Institute and the Danish Patent and Trademark Office. Ørsted was the first modern thinker to explicitly describe and name the thought experiment.

In 1825, Ørsted made a significant contribution to chemistry by producing aluminium for the first time. While an aluminium-iron alloy had previously been developed by British scientist and Inventor Humphry Davy, Ørsted was the first to isolate the element via a reduction of aluminium chloride.

In 1829, Ørsted founded Den Polytekniske Læreanstalt ('College of Advanced Technology') which was later renamed the Technical University of Denmark (DTU).

Ørsted died at Copenhagen in 1851, aged 73, and was buried in the Assistens Cemetery in the same city.

A leader of the Danish Golden Age, Ørsted was a close friend of Hans Christian Andersen and the brother of Politician and jurist Anders Sandøe Ørsted, who served as Prime Minister of Denmark from 1853 to 1854.

The Ørsted Park in Copenhagen was named after Ørsted in 1879. The streets H.C. Ørsteds Vej in Frederiksberg and H. C. Ørsteds Allé is located in Galten are also named after him.

A statue of Hans Christian Ørsted was installed in the Ørsted Park in 1880. A commemorative plaque is located above the gate on the building in Studiestræde where he lived and worked. The 100 danske kroner note issued from 1950 to 1970 carried an engraving of Ørsted.

The first Danish satellite, launched 1999, was named after Ørsted.