The former France international ends his four-and-a-half years at Ewood Park after signing for his hometown club.
Signed initially on loan in January 2009 from Olympique Marseille, impressive defensive displays saw Rovers make the move a permanent one that summer.
A fans favourite for his wholehearted displays both at left-back and in the centre of defence, Givet went on to make 133 appearances, scoring five goals.
"I want to say thank you to the club and to the fans," said Givet.
"Before Blackburn, I enjoyed my football in Monaco - I played in the Champions League final - but my first three years in the Premier League with Blackburn were the best moments of my career.
"It was an amazing experience for me and one I will never forget. Blackburn Rovers will always have a big place in my heart and I am sad to be leaving, but last season was hard for me and I think it is better for me and my family to go back to France.
"But once again, I say thank you to the club for giving me a chance to play in England and thank you to the fans for your support - I will never forget it."
Rovers boss Gary Bowyer paid tribute to the Frenchman, adding: "Gael was very popular amongst the supporters, because he always gave 100%, which is something we’re trying to get back to now.
"We have all enjoyed his warrior-like performances over the past four-and-a-half years and the 1-0 victory at home to Huddersfield last season, which was the one full game he played for me, I thought he was outstanding.
"We’re sad to see him leave, but he was eager to return to France and he wants to play more football at this stage in his career, which we fully understand, so I think this is the best solution for both parties."