The reality TV star died with her mother Jackiey Budden at her side at her home in Upshire, Essex, at 3.14am on Mother's Day.
"My beautiful daughter is at peace," Ms Budden said.
Speaking outside her home, wearing pyjamas with a coat over the top, she added: "Family and friends would like privacy at last."
Referring to how her public battle with cancer has raised awareness of the disease, Mr Clifford said: "I think she's going to be remembered as a young girl who has, and who will, save an awful lot of lives.
"She was a very, very brave girl.
"And she faced her death in the way she faced her whole life - full on, with a lot of courage."
He said it was "ironic" that the 27-year-old - who had two young sons Bobby, five, and Freddie, four - had died on Mother's Day.
Mr Clifford said he hoped Goody's family would now be left in peace to grieve.
Goody's friend Kevin Adams, who was also there when she died, left the house visibly upset and dressed all in black this morning. He declined to comment to reporters outside the home.
Goody's body was taken out of her home and placed in the back of an estate car shortly before 8am.
Mourners started arriving at the house to pay tribute to Goody within minutes of the news breaking. They left floral tributes at the gates of her home.
Later, two police officers arrived at the house.
Harpal Kumar, Cancer Research UK's chief executive, said: "We are very sad to hear of Jade's death and our thoughts are with her family and friends at this devastating time.
"Her brave battle with an aggressive form of cervical cancer has received widespread public attention and encouraged thousands of women to seek advice on how to prevent the disease.
"It's critical that young women take up their invitations to cervical screening if we are to avoid more tragic cases like Jade's. She has done a great public service by raising awareness of the importance of screening during her last few months of life.
"Jade is one of 1,000 women to die from cervical cancer each year in the UK.
"Every death from cancer is a tragedy and Cancer Research UK is absolutely determined to reduce the number of people dying from the disease.
"We've set an ambitious five-year strategy to achieve this and plan to spend £300 million a year over the next five years to gain a better understanding of cancer, improve prevention and screening, diagnose cancer earlier and develop better treatments."
Dr Lesley Walker, Cancer Research UK's director of cancer information, added: "Cervical screening is very important because it can stop cervical cancer from developing in the first place. It is one of the few preventable cancers because pre-cancerous cell changes can be picked up before they have a chance to develop into a full blown cancer.
"Women can protect themselves against cervical cancer by always attending routine screening tests when invited by their doctor. These tests detect any changes in the cells lining their cervix early on, so they can easily be treated before cancer develops.
"In the long term, the introduction of the cervical cancer vaccine has the potential to prevent cervical cancer in the UK. The vaccine is being offered to all 13 year old girls in UK schools - with a catch up programme for girls aged up to 18. Parents can help protect their daughters against cervical cancer by ensuring they receive the vaccine."
Mr Clifford later said that Goody's new husband Jack Tweed was with her when she died.
He said: "Jack has been absolutely amazing, nursing her to the end."
He added: "She died having been in a deep sleep for the past 24 hours. Jack was there and her mum was there.
"It is ironic that she died on Mother's Day after she was such a good mum, she is a wonderful mum and so determined to secure the best possible future for her boys."
He said that Goody had told her boys when she and they were Christened at the beginning of the month that, "by getting to know Jesus they can stay in touch with their mum."
A spokesman for TV presenter Jeff Brazier, the father of Goody's two sons, said: "He is extremely sad to hear of Jade's passing and obviously his priority now is going to be with his boys."
Later Mr Adams - who was Goody's friend and personal trainer - told journalists that no funeral arrangements had been made.
He said Goody's mother wanted to spend time with family and friends so that she could grieve privately.
"She would just like this time for family and friends for private grieving," he said. "Thank you very much."
Commenting further, Mr Brazier said: "I'm devastated to learn Jade sadly left us on Mother's Day.
"I'm grateful the boys were able to say their goodbyes and spend that precious time with their wonderful mother.
"Bobby and Freddie are my absolute priority and I will be doing everything I can to be their rock and to give them all my love and support to get them through a confusing and upsetting time."
The presenter, who has been working on The X Factor Live tour in between being with his family, will now take some time off, according to a spokeswoman for the tour.
Mr Brazier added: "We thank everyone for their strength and love and we want you to know that we are determined to get through this as well as we can."
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