Born to a farmer's family[2] in the small village of Zagorica east of Ljubljana in Slovenia, Vega was 6 years old when his father Jernej Veha died.

Tentamen philosophicum, a list of questions for his comprehensive examination, was preserved and is available in the Mathematical Library in Ljubljana.

Vega left Ljubljana five years after graduation and entered military service in 1780 as a professor of mathematics at the Artillery School in Vienna.

When Vega was 33 he married Josefa Svoboda (Jožefa Swoboda) (1771–1800), a Czech noble from České Budějovice who was 16 at that time.

In 1788 he served under Austrian Imperial Field-Marshal Ernst Gideon von Laudon (1717–1790) in a campaign against the Turks at Belgrade.

In 1795 he had two 30-pound (14 kilogram) mortars cast, with conically drilled bases and a greater charge, for a firing range up to 3000 metres (3300 yards).

An engineer, Franc Allmer, honourable senator of the Graz University of Technology, has found Vega's logarithmic tables with 10 decimal places in the Museum of Carl Friedrich Gauss in Göttingen.

A copy of Vega's Thesaurus belonging to the private collection of the British mathematician and computing pioneer Charles Babbage (1791–1871) is preserved at the Royal Observatory, Edinburgh.

Over the years Vega wrote a four-volume textbook Vorlesungen über die Mathematik (Lectures about Mathematics).

Although he worked in the subjects of ballistics, physics and astronomy, his major contributions are to the mathematics of the second half of the 18th century.

In 1781 Vega tried to push further his idea in the Austrian Habsburg monarchy about the usage of the decimal metric system of units.

Jurij Vega High School (Gimnazija Jurija Vege) in Idrija was founded in 1901 as the first Slovene Realschule.