He reassured fans his surgery went well and last month has “been at home, recuperating, recovering and resting and getting some post-op treatment as well”.
He added that he feels “great right now” and “ready to come back”.
“I feel energised and almost back to myself, yes I’ve had a really serious situation but I’ve come out the other side at this point and I feel great. I feel raring to go and I feel in good health.”
Dan Knowles, chief executive at the charity Brain Tumour Research, external, said: “Every day, 35 people are diagnosed with a brain tumour.
“We thank Trevor for sharing his diagnosis and treatment, helping to raise awareness of this disease and the impact it has on families across the UK. We are thinking of him and wishing him well as he navigates this journey.”
The father-of-two said he is back to doing things he enjoys like playing golf and going to the gym.
He urged fans not to worry about him and thanked everyone for their love and support.
Nelson, who presents a weekday afternoon show on Radio 2 and appears on 1Xtra late on a Sunday morning, celebrated 30 years at the BBC earlier this year.
