The Belgian footballer died at the age of 28 after a long battle with leukaemia.
Following the news on Tuesday, Van Damme's Belgian top-flight club said words were not enough to describe what they felt.
Five years ago, the goalkeeper was first diagnosed with the disease.
"It is with great sadness we report that our friend and team-mate Van Damme has fought his long and uneven battle against leukaemia," the club said.
Perseverance and strength to go for it over and over was admirable.
You are an example of persistence and fighting spirit. A source of inspiration. In our green-black heart, #16.
Van Damme was initially diagnosed with leukaemia during a medical prior to the 2016-17 season, but the disease returned again in 2019.
He and his wife became parents to a child.
Dobbelaere wrote on Instagram: "Our dearest darling, daddy left for his last match last night, a match that can no longer be won. You left us very slowly, yet you did it again in your own way… very strong.
You fought like a lion. We are very thankful for who you were. An example for others. You have made me realize that there is no such thing as giving up, even if you only have a small amount of success.
Rest now darling, you have more than earned it, you are free from all the pain.
The Belgian Pro League said: "Our thoughts are with his family, friends and everyone at Cercle Brugge.
Your fighting spirit has been inspiring. Rest in peace.