Ekeberg, who was born in the Swedish capital of Stockholm, graduated from the University of Uppsala in 1788 and, after traveling in Europe, began teaching chemistry at Uppsala in 1794. He was an early convert to the system of Antoine Lavoisier and introduced this new chemistry to Sweden. He was partially deaf from a childhood illness but the further loss of an eye (1801) caused by an exploding flask did not impede his work.

Ekeberg is remembered chiefly for his discovery of the element tantalum. In 1802, while analyzing minerals from Ytterby quarry, Sweden, he isolated the new metal. The name supposedly comes from its failure to dissolve in acid, looking like Tantalus in the waters of Hell. It was a long time before it was recognized as a separate element as it was difficult to distinguish from niobium, isolated by Charles Hatchett in 1801. Wollaston failed to distinguish between them and it was as late as 1865 that Jean Marignac conclusively demonstrated the distinctness of the two new metals.