The 28-year-old captained Australia against Wales in 2024, Joe Schmidt promoting the flanker in what was the coach's first Test in charge and Wright's first Test in four years.
Recurring shoulder issues meant he barely played again the following season, the uncontracted, tough-as-nails former Queensland Reds skipper returning to club rugby with Easts this year in a low-profile return.
But ahead of next year's World Cup in Australia, the six-Test back-rower will make a professional return with Ospreys.
He's set to join former Reds teammate and lock Ryan Smith in the United Rugby Championship that features teams from Ireland, Italy, Scotland, South Africa and Wales.
"I'm excited to get started with this new chapter at the Ospreys," Wright said.
"I've actually got a bit of Welsh heritage, my grandfather was born in Pembroke, so I know it's a club with a rich history and passionate supporters.
"I had a chat with Ry (Smith) when I started to consider the move and he spoke so highly of the place and the boys that are there.
"This is a great opportunity for me to test myself in new waters."
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