Valeri, 29, had been a Socceroo regular under Holger Osieck and was on course to feature in Italy's top flight after watching his team-mates gain promotion during a long stint on the sidelines last season.
The holding player, who suffered a leg injury on international duty in November 2012, has been named on the bench for Sassuolo in recent months, but proved unable to force his way back into the first team.
And the former Internazionale youth team player, who spent five years with Grosseto, has now dropped down a division to struggling Serie B outfit Ternana in a bid to earn regular playing time.
Capped 50 times for Australia, Valeri's injury woes make him an outsider to gain a spot on the plane to Brazil later this year, but a good second half of the season could make national coach Ange Postecoglou sit up and take notice.
