The presenter and broadcaster said producers of the ITV show had been “so good” with duty of care and had been adamant that he be checked out properly after becoming ill.
The 65-year-old was taken to hospital as a precaution after falling ill at Gwrych Castle in North Wales in the early hours of Thursday.
Joining co-hosts Ant McPartlin and Declan Donnelly for an exit interview, Madeley said: “I feel as fit as a fiddle and I am fit as a fiddle.
“And you know if it wasn’t for Covid I’d be back there sort of eating rice and beans.
“(Covid) is still biting our bums, isn’t it? What happened was I had just a funny little turn quite sort of late in the morning.
“ITV are so good with duty of care. They were adamant.
“They said, ‘No, we have to make sure that you’re OK.’ I said, ‘But I am OK.’ They said, ‘We have to make sure.’
“So I went to the local hospital – I was only in there for about an hour-and-a-half – I was given really thorough checks and I was given a completely clean bill of health.
“No matter what you might have read, I’m absolutely fine.”
Madeley admitted he had hung around briefly at the hospital after being discharged in order to get a large cup of tea and a bacon sandwich.
“That was my first port of call… it was amazing,” he said.
“I ate hospital food, exactly… as I say, if it wasn’t for Covid, I’d still be in the game. I’m gutted. I’m gutted, I really am.”
Madeley also recorded a message for his former campmates explaining his departure which was played to them during Friday’s show.
“My adventure is over,” he told them.
“I just want to say how much I love you, you know I mean that and how much I’m grateful to you for everything you’ve said and done for me over the past few days and I’m going to set up that WhatsApp group we spoke about for when you come out.
“We can all talk to each other again and hopefully meet up.
“Anyway, I’ll be watching over the next few weeks and I wish you all the love and luck in the world, I can’t wait to see who wins.”
Singer Frankie Bridge replied tearfully: “Of course he did the perfect video.”
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Fellow broadcaster Louise Minchin told the Bush Telegraph - where the celebrities film their confessionals: “We saw his face, we saw how he was, we saw Richard back to his cheery, brilliant, funny self.”
It is understood Madeley will not be replaced by another celebrity.
Friday’s episode was broadcast as a pre-recorded show rather than live due to concerns over Storm Arwen, which was due to hit the area near to the castle around 9pm.
It is understood Ant and Dec recorded their links early in the evening as part of “precautionary measures” being put in place by ITV following severe storm weather warnings.
A spokesperson for I’m A Celebrity said: “Tonight’s I’m A Celebrity… Get Me Out Of Here! will be broadcast as a pre-recorded show rather than live due to the developing Storm Arwen and precautionary measures we’re putting into place on production.
“Our celebrities will remain inside the castle, which is secure, and we have contingencies in place to cover all weather scenarios to ensure the safety of our cast and crew.”