Mr Brown added that prescription charges for other long-term conditions will also be phased out, although he did not say when.
The new health policy was part of a speech outlining his vision for a fair society in the UK.
Speaking in Manchester yesterday, he told delegates: 'Because we know that almost every British family has been touched by cancer, Alan Johnson and I know we must do more to relieve the financial worry that so often goes alongside the heartache, so our plan is next year to abolish all prescription charges for everyone with cancer.
He added: 'And this is not the limit of our commitment to a fair NHS. In the long term, as the NHS generates cash savings in its drugs budget, we will plough them back into abolishing charges for all patients with long-term conditions.'
Mr Brown also praised nurses and other NHS staff. He said: 'Now, as we celebrate the 60th anniversary of the NHS, let me on behalf of all of us here, and all the people of the country - thank all the NHS staff - the cooks and cleaners, the paramedics and porters, the doctors and midwives and nurses.
'You have served our country and served a great ideal - the principle that in a fair society health-care should not be a commodity to be bought by some but a right to be enjoyed by all,' he said.
Mr Brown also praised NHS staff for their work cutting MRSA rates in hospitals by 36% since last year.