Born in Logroño, Spain, D'Elhuyar studied mineralogy with his brother, Juan José, at the Freiberg Mining Academy under Abraham Werner. He then studied chemistry in Paris (1772–77). He returned to Spain shortly after and was sent to Mexico in 1788 to supervise mining operations. On his return to Spain in 1821 he was made director general of mines.

The D'Elhuyar brothers working together in 1783 discovered the element tungsten (formerly also known as wolfram). Two very dense minerals were known to chemists in the 18th century: ‘tungsten’ (Swedish meaning ‘heavy stone’) and wolframite. In 1781 Carl Scheele had discovered that ‘tungsten’ (now known as scheelite) contained tungstic acid. The brothers proved that the same acid is present in wolframite, from which mineral they succeeded in isolating the element tungsten.