The 22-year-old has now joined the team which pipped them to promotion from League One last season.
The Bees are entitled to compensation as Forrester is under 24 but a fee has not yet been agreed and a tribunal may be required.
Brentford sporting director Mark Warburton told the club website: "We would like to thank Harry for his service and commitment over the last two seasons.
"We wish him well for his future career.
"Whilst sorry to see Harry depart Griffin Park, it simply underlines the fact that whilst we as a club will move to attract and secure talented individuals, we only want players who are absolutely committed to Brentford FC.
"We will make very positive and aggressive offers to retain the services of key staff, but not seek to break the pay structures that we think are appropriate."