The singer was diagnosed last year after two tumours - including one the size of a golf ball - were found at the back of his tongue.
"You can imagine to get rid of that with radiation - the inside of my head has been cooked pretty effectively," he told the BBC.
He added although his voice was fine, it will take a while "to heal up".
"I can sing, I can talk - I haven't gone out and done the equivalent of trying to run 100 metres in the same way I used to sing before," he told the BBC's Colin Paterson.
"I only finished coming out of treatment two months ago and the doctor said it will take a year to be better.
"We've beaten that by about six months so far, but I'm not going to push things to prove a point."
Iron Maiden announced in May the band would not be touring or playing any shows until next year when Dickinson will be "back to full strength".
The singer said since he was given the all clear by doctors, he was now "looking forward to having a bit of a knees up" because "it's a good excuse to celebrate a wonderful thing".
"I've been through what a load of people go through every day," he said.
"There's thousands of people every day in the UK and around the world who have treatment for this kind of thing. In that respect the only thing that's special about it is that I'm quite a well-known person. I've been very fortunate. I've had a really good bounce back."
Talking about when he was first diagnosed with cancer, Dickinson said the only symptoms he had noticed was a lump in his neck - cause by the second, smaller tumour.
"I went to the doc and he went 'oooh that's a bit weird'," he said.
"He took a scan of it, had a look, had a poke around, and went 'you have head and neck cancer'. So I went 'that's a bit of a blow' - but you crack on and you get on with it."
Dickinson was speaking at the Silver Clef Awards in London, where Iron Maiden were honoured for their outstanding contribution to UK music.
Other winners at the event - in aid of charity Nordoff Robbins - included Rita Ora, who was named best female, best male Jake Bugg and James Bay who won best newcomer.
Arctic Monkeys were also voted best live act of the year, Kasabian won best group, Gladys Knight collected the international award and Duran Duran were honoured with the lifetime achievement award.
Iron Maiden frontman Bruce Dickinson has said he is healing well since being treated for cancer earlier this year.