"I'm sure he'll come through this," said Mr Cameron, adding how Mr Johnson is a "very tough, very resilient, very fit person."
Mr Cameron, who went to the same school as Mr Johnson, said he knows how fit his friend is from "facing him on the tennis court".
The Prime Minister was taken to St Thomas' Hospital in London on Sunday night "as a precaution" after his coronavirus symptoms persisted but was taken to intensive care on Monday afternoon after they worsened.
But he is "stable" and in "good spirits" after receiving oxygen treatment for Covid-19, his official spokesman said on Tuesday morning.
- Dr Alison Pittard explains the kind of treatment Boris Johnson can expect in intensive care
Senior Cabinet minister Michael Gove told LBC: “He is kept, of course, under close supervision.
"By being in intensive care if there is further support he needs it is there at hand. But the Prime Minister has not been on a ventilator.”
Mr Cameron said his friend the prime minister has a "tremendous zest for life" and will "want to get well and get in charge again".
He said he is "hoping and praying" Mr Johsnon "gets well soon and gets back to Number 10 where I know he wants to be and where we all want him to be".
He added: "He's doing a tremendous job and obviously we all want him back in there."
He was echoed by Mr Johnson's predecessor Theresa May, who said her "thoughts and prayers" are with the prime minister.
She added: "I wish him well and I want him to have a speedy and good recovery."
Mr Cameron said there's a "very good system in place" in British politics that means decisions will continue to be made, regardless a prime minister's condition.
"If he or she can't take a decision then the number ten team pare that decision and it can be made by the deputy.
"In this case Dominic Raab the first secretary of state. So there's a very good system in place.
"The civil service is a great machine, professional, impartial, good at preparing these decisions, and the right decision I'm sure will be taken."
On Tuesday, in the absence of the PM, Mr Raab chaired the Government's daily emergency coronavirus meeting.
Cabinet minister Brandon Lewis, who was part of the daily Covid-19 meeting, said despite Mr Raab standing in, Mr Johnson is "still the prime minister".
He told ITV News: "The prime minister has given a very clear lead, and he is fully conscious.
- Dominic Raab arrives at Number 10 to chair the coronavirus meeting:
"It's important for people to be very aware of the fact he's still the prime minister, he's very much conscious but Dominic, yes, who is empowered as the first secretary of state, has been asked to stand in and deputise, by the prime minister."
A spokesperson for No.10 said on Monday evening: “Since Sunday evening, the Prime Minister has been under the care of doctors at St Thomas’ Hospital, in London, after being admitted with persistent symptoms of coronavirus.
“Over the course of this afternoon, the condition of the Prime Minister has worsened and, on the advice of his medical team, he has been moved to the Intensive Care Unit at the hospital."
The spokesman added: "The PM is receiving excellent care, and thanks all NHS staff for their hard work and dedication."
The Queen has been kept informed about the Prime Minister's condition by Downing Street, Buckingham Palace said.
Mr Johnson was moved to the ICU (intensive care unit) at St Thomas’ at around 7pm on Monday night after his condition worsened over the course of this afternoon, the spokesperson said.
He has been moved to the ICU as a precaution should he require ventilation to aid his recovery, they said.
The Prime Minister "remains conscious at this time", the spokesperson said.
Speaking on Monday evening, Mr Raab said the Prime Minister was in "safe hands" and was receiving "excellent care" at St Thomas' Hospital.
"The Government's business will continue," he said.
- Boris Johnson's friend and former Director of Communications outlines how he thinks the Prime Minister will have reacted to his condition worsening:
Politicians from all-parties expressed their support for the Prime Minister.
Newly elected Labour leader Keir Starmer gave his best wishes to Mr Johnson and said his party will work "constructively" with the Government to get through the coronavirus crisis.
"I know I speak on behalf of the whole country when I say our thoughts with the Prime Minister, his fiance and his family," he said.
"We have amongst the best staff doctors and nurses in the world in the hospital he is in so I know he will be well looked after. But people are clearly anxious.
"I know the business of government will continue. I was in touch with the Foreign Secretary last night, and I want to say that the Labour Party will act in the national interest.
"That's why I have offered to act constructively with the Government and support them where that's the right thing to do, and push them further where we need to do it."
Labour former prime minister Gordon Brown said he is "as worried about the Prime Minister as everybody is".
He told BBC Radio 5: "Well I feel very sorry for Boris Johnson because the worst thing that can happen to someone who is a leader is that they are incapacitated at the time when their leadership is needed most and I wish him well. I hope his recovery will be swift and I hope he'll get back to full health."
Scotland First Minister Nicola Sturgeon tweeted: "My thoughts are with the PM and his family - sending him every good wish."
Chancellor Rishi Sunak tweeted: "My thoughts tonight are with @BorisJohnson and @carriesymonds. I know he'll be getting the best care possible and will come out of this even stronger."
Coronavirus: Everything you need to know