Jónsson was born in Iceland. Though he was born into a poor Icelandic family, the young Vilhjálmur Jónsson was a linguistic prodigy, learning Danish, Greek, and Latin on his own at an early age. By the end of his life he was reported to be able to speak twenty-eight languages. This talent was recognized early, and he was sent to Denmark to study at the university in Copenhagen, where he studied law.
In 1783, he was appointed to the supreme court of Frederiksnagore. There he was entranced by Indian culture, a then-untouched field of European scholarship, and he founded the Kongelige Danske Østindiske Selskab (Royal Danish East Indian Society) in 1784 - the first learned organisation in India to study Asian civilization scientifically. Over the next ten years he would produce a flood of works on India, launching the modern study of the subcontinent in virtually every social science. He also wrote on the local laws, music, literature, botany, and geography, and made the first Danish translations of several important works of Indian literature.
Of all his discoveries, he is best known for noticing that Sanskrit bore certain resemblances to Latin and Greek. He summed up the nature and implications of his findings in his 1786 address to the Kongelige Danske Østindiske Selskab. He suggested that all three languages had a common root. This discovery led to several decades of intensive historical-comparative work and to important advances in historical linguistics during the nineteenth century.