Former player Luke Robinson will be in charge of Huddersfield for Thursday's rearranged Betfred Super League game against Wakefield following the sudden departure of head coach Simon Woolford.
The Giants announced on Monday that the 45-year-old Australian would not be offered a new contract when his current deal runs out at the end of the season and they have brought forward his departure.
Huddersfield managing director Richard Thewlis said: "Simon and I caught up today regarding the position and we both agreed this is best for both parties."
Thewlis says the club have already received several expressions of interest in the vacancy.
The Giants are eighth in Super League but without a win since the season restarted on August 2.
Woolford, a former Newcastle Knights assistant coach, was appointed by Huddersfield in April 2018 with the club bottom of the table and battling to avoid relegation.
He guided them to safety and they started the 2020 season with four wins from five league games.
However, since the campaign's resumption following the five-month break because of the coronavirus pandemic, they have lost all five matches, three of them by a solitary point.
Thewlis added: "I would like to pay tribute to Simon for his professionalism and realisation of the situation once it was known he wasn't seeking an extension and everyone here wishes him and his family every success in the future.
"He returns to Australia after just over two years experience here as head coach and I am sure will have many suitors down under for his services "