The former Tottenham manager takes charge of a Riyadh-based side captained by Portugal forward Cristiano Ronaldo. Al-Nassr won the Saudi Pro League title for the first time in May.
They were previously coached by veteran Portuguese coach Jorge Jesus, who left the club at the end of the campaign.
Postecoglou has been out of work since he was sacked by Nottingham Forest last October, having lasted just 39 days in charge.
The 60-year-old, who was born in Greece and represents Australia, has signed a two-year contract with Al-Nassr. Postecoglou guided Tottenham Hotspur to Europa League glory in 2025.
He had previously enjoyed a successful spell at Celtic, winning back-to-back Scottish Premiership titles. Postecoglou has spent recent weeks working as a pundit with ITV during the World Cup.
His appointment ends a nine-month spell out of management and hands him his first job outside Europe.
It also reunites him with a dressing room built around Ronaldo, who remains Al-Nassr's captain following last season's title triumph.