The 24-year-old left international duty with Wales last week and after medical examinations, it has been confirmed that he has Stage II Hodgkin Lymphoma.
He will undergo treatment next week after an initial positive prognosis.
In a statement issued via Bournemouth' s website, Brooks said: "This is a very difficult message for me to write.
"I have been diagnosed with Stage II Hodgkin Lymphoma and will begin a course of treatment next week.
"Although this has come as a shock to myself and my family, the prognosis is a positive one and I am confident that I will make a full recovery and be back playing as soon as possible.
"I'd like to show my appreciation to the doctors, nurses, consultants and staff who have been treating me for their professionalism, warmth and understanding during this period.
"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.
"I'd also like to say thank you to AFC Bournemouth for all their support and assistance this past week.
"Although I appreciate that there will be media attention and interest, I would like to ask that my privacy is respected in the coming months and I will share updates on my progress when I am able to do so.
"In the meantime, thank you to everyone for their messages of support – it means so much and will continue to do so in the months ahead.
"I look forward to seeing you all again and playing the sport I love very soon."
Warrington-born Brooks joined Bournemouth from the Blades in July 2018 in a £12m deal after bursting onto the scene in outstanding fashion at Bramall Lane.
The midfielder made an immediate impression in the Premier League with the Cherries, scoring seven goals in 2018-19. He was nominated for the PFA Young Player of the Year award which was eventually won by Raheem Sterling.
Brooks missed much of the 2019-20 season with an ankle injury - in a season which ended in relegation from the Dorset outfit.
He was subsequently linked with a return to Bramall Lane, but stayed on the south coast.
Brooks started his career at Manchester City before switching to the Blades academy in 2014 and signed professional forms with the club in March 2015.
He spent a short loan spell at Halifax in August 2015 and made his United debut in an EFL Trophy tie 12 months later.
Brooks scored his first senior goal in the Blades' 2-1 victory at Yorkshire rivals Leeds United in October 2017 and soon developed a reputation as one of the hottest young properties in the EFL.
Bournemouth chief executive Neill Blake added: "Everyone at AFC Bournemouth will do everything possible to help support David and his family during his recovery.
"We’re not putting any timescales on his return; we will give David all the time he needs to get well and will do everything that we possibly can to help with that.
"I know everyone will be keen to show their love and support for David which will help him immensely as he recovers, but we also urge you all to respect his and his family’s privacy during this time."
A message on the Blades Twitter account said: "We’re all behind you, @DRBrooks15. Get well soon, you’ve got this."