Brooks, who has made 21 appearances for Wales, withdrew from their squad last week and thanked their medical team for helping diagnose the illness.
"I have been diagnosed with Stage 2 Hodgkin Lymphoma and will begin a course of treatment next week," Brooks said in a statement on Bournemouth's website.
"Although this has come as a shock to myself and my family, the prognosis is a positive one and I'm confident that I will make a full recovery and be back playing as soon as possible.
"I want to thank everyone at the Football Association of Wales because without the swift attention of their medical team we may not have detected the illness."
Hodgkin Lymphoma is a cancer of the lymphatic system, an important part of the immune system.
Bournemouth chief executive Neill Blake said that the Championship club would not put a timescale on his return.
"We'll give David all the time he needs to get well and will do everything that we possibly can to help with that," he added.