The 23-year-old has one year remaining on his contract with the Premier League club.
He managed 10 goals in 14 games from March, and will be hoping that form can find him a starting spot at another team next term.
Writing on social media after the season ended, Hirst said: "Forever grateful for the opportunity to have played for your amazing club, to all the fans who have supported me this season through good times and bad, to the staff for helping me improve as a player, and to all the boys I've shared the pitch with this season who have made me feel a part of the family, it's been a pleasure. I can't thank you all enough. Time to rest up and see what the future holds."
On Hirst, Portsmouth manager Danny Cowley has said: "George has done great and really kicked on in the second-half of the season.
"He is continuing to grow and we have worked really hard with him, and I want to give him the credit because he came off the back of a difficult season at Rotherham United.
"He had an injury and was probably five or six weeks behind the group physically. He has worked really, really hard to find this form and we are proud of him.
"We see him as a No.9 and one that can be a top player at this level. This is the quality of player that you need in this division."
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