The 26-year-old joined on a free transfer from West Bromwich Albion in the summer of 2015 and had scored once in 30 appearances for the Terriers, but he found himself out-of-favour at the club following the arrival of manager David Wagner in November of that year.
It is understood that Davidson sat down the hierarchy at Huddersfield and both player and club agreed to a mutual termination of his contract in order to pave the way for a move to Rijeka.
The Croatian side will feature in this season’s Europa League after missing out on UEFA Champions League qualification last week after a 3-1 loss to Olympiacos.
Hopes for the 2018 World Cup
The Australian has one eye on the Socceroos squad for the World Cup next year in Russia but has not played for the national team since November 2015 - despite previously being a key player under head coach Ange Postecoglou.
The defender, who has 23 caps for his country, was a part of the squad that won the Asian Cup in 2015 and even scored in the 2-0 win in the semi-final over the United Arab Emirates.
Davidson was also included in the Australia squad for the 2014 World Cup in Brazil and played in all three games in the group stage as Postecoglou’s side were defeated by Chile, Netherlands, and Spain.
No permanent return to the Netherlands
Davidson spent last season on loan at FC Groningen, making 22 appearances, and helped Ernest Faber’s side to an eighth-place finish in the Eredivisie.
He previously had a three-year spell in Holland with Heracles before moving to England with West Brom and was largely successful at the Polman Stadion, scoring twice in 51 appearances.
There was an option in the loan deal to make the move permanent but Groningen decided not to activate the clause and Davidson had no choice but to return to Huddersfield.
The defender did not feature in any of Town’s first-team pre-season friendlies and instead trained with the club’s development squad.