The German is currently with Haas, who announced his departure earlier and have been linked to Ferrari-backed Briton Oliver Bearman.
Sauber will become the Audi factory team in 2026.
"The prospect of competing for Audi is something very special. When a German manufacturer enters Formula 1 with such determination, it is a unique opportunity," said Hulkenberg.
"To represent the factory team of such a car brand with a power unit made in Germany is a great honour for me."