Vox opposes illegal immigration and Catalan independence.
"The Andalusians have made history ... and got rid of 36 years of socialist rule," said Vox leader Santiago Abascal.
The French far-right leader, Marine Le Pen, sent her "warm congratulations" to her Spanish counterparts.
The Socialist party won 33 seats to record its worst result. It will be unable to form a majority even in coalition with leftwing allies.
The poll in Andalusia, Spain’s most populous region and among its poorest, had been considered as the first of several tests for socialist prime minister Pedro Sanchez.
He took office in June after winning a surprise vote of no-confidence in parliament against the previous Popular party government of Mariano Rajoy over a corruption scandal.
Reacting to the Vox success, Sanchez, who is in Poland for the COP 24 climate summit, tweeted that the result in Andalusia would increase his efforts to defend the constitution and democracy.