The monarch, who died aged 96 on Thursday at Balmoral in Scotland, was patron of the Scout Association.
Grylls, who was awarded an OBE by the Queen in 2019, said the Scouts family are “united in sorrow for the loss of our Patron” and that she leaves a “bright legacy of hope and promise for future generations”.
The 48-year-old spoke to the PA news agency on Friday about his memories of the Queen, what scouting meant to her and how the organisation is ready to evolve as King Charles III takes the throne.
Grylls said: “I was lucky to meet the Queen on a bunch of different occasions – from the amazing evenings she hosted for Explorers at Buckingham Palace to sitting next to her at dinner one time and she did my OBE.
“The times I met her, the times she lit up the most, was whenever we did something Scouting.
“I think it was one of the organisations she was most proud to represent.”
Grylls said the Queen had told him several times how she loved volunteering and remembered it as a young girl during the war.
He added that she “championed” young people in the UK throughout her life and was “especially proud” when girls were first able to join the Scouts in the 1970s.
The Queen was also “so generous” to the Queen’s Scouts – the highest award Scouts can receive – every year at Windsor Castle, Grylls said.
“I remember especially in 2012 driving her up and down the ranks as she inspected all the Queen’s Scouts,” he said.
“This was the time when her face was just a huge beaming smile from start to finish.
“She just loved seeing young people get opportunities and skills routed in old fashioned values like kindness, loyalty, friendship and respect that never go out of fashion.”
Grylls also spoke of how the Scouts have seen their biggest growth in the past year since the Second World War.
“To leave the organisation she was patron of all her life, leave it in such strong measure, is a really big testament to her,” he said.
“She always treated people the same, gave them time, listened to them, she had a wit in her and was always ready to laugh at the drop of a hat.”
On how the organisation will adapt as Charles becomes King, Grylls said the Scouts are “great at embracing change”.
“I think one of the characteristics of Scouts is that it is always evolving, listening and adapting,” he said.
“Kids are often better with change than adults and the Scouts are always great at embracing change.
“We will be seeing our promise to the King and that strong continuation of life and service – Scouts are always rooted in service.
Grylls said the Queen would have wanted everyone to look ahead rather than dwell on her passing, adding: “The future is always brought to life in the faces and hearts and actions of young people.
“She would have wanted all of us to look to the future.”