The 45-year-old will depart the John Smith’s Stadium upon the completion of his two-and-a-half year contract after he first joined the club from Newcastle Knights’ Intrust Premiership side in April 2018.
The Australian admitted last week that he was unlikely to remain at Huddersfield following the conclusion of the prolonged 2020 campaign.
The Giants have already had candidates step forward for the position and the club’s managing director, Richard Thewlis, said: “It felt best for all to get this news out now so we can concentrate on the specific task in hand, which is getting our first win since lockdown and supporting Simon and the squad in achieving their goals for the end of the year.
“We have already begun to receive expressions of interest for the head coach’s role starting 2021, which we will deal with in due course.
"We would like to thank Simon for his service to the club and we hope he can finish his time with us with the success that we all desire.”
Huddersfield are without a win in all five of their matches since the Super League season restarted, three of which have been lost by a single point.
Woolford admitted last week he would have liked to remain at the Giants for a longer period but is proud of the job he has done.
“When I took this job on I always anticipated it being a three to four year job. I’ve been here just over two years now and feel like we’ve made a lot of inroads with our squad,” he said.
“We’ve had to make a lot of changes over the last couple of years.
“When I first got here it was pretty dire; the club was looking at relegation but we had a nice run of games when I got here in ‘18 and last year we were cut down by injury and it was a tough year.
"But looking at our squad now and all things being equal, it’s a squad that can compete for trophies in Super League.”
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