Archie Vaughan, who was born on Christmas Day 2017, died at home in Morley on Sunday (Nov 7).
Archie underwent surgery in July to try to remove a tumour from his brain stem.
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Following the operation, Archie's parents Hayley and Craig decided not to put him through more treatment and chose to make his remaining time as happy as they could with siblings Lily, 11, and Harry, six.
Hayley and Craig said "Friends, family and the community helped us to make memories with Archie.
"We managed to take him to Spain for a holiday in the summer which he just loved being in the pool all day every day.
"We went to Scarborough with him to his favourite beach, and also on a two night Disney cruise.
"We treasure some amazing memories from the last six months.
"In the last few weeks we went over the top with Halloween decorations and put up Christmas trees early.
"Although he could no longer play he loved looking at the lights."
The couple added: "Archie was such a happy, kind, sweet little boy.
"He was always smiling. He was very caring and full of fun.
"Archie passed away so peacefully Sunday morning snuggled up in bed with his mummy and daddy.
"The Saturday night he had watched fireworks and been for a little walk in his buggy.
"The kindness we have received from so many people and many we haven't even met has been so overwhelming and it's too hard to thank people individually.
"We have been supported hugely by our Macmillan nurse. We couldn't have got through this without him.
"Also Candlelighters have been amazing. What they offer to families is actually something quite special and I never realised until now what the charity actually does.
"They have provided so much support to us and our other two children in so many different ways.
"In lieu of flowers we are asking for donations to Candlelighters if anyone would like to donate that would be hugely appreciated, raising money for them will now always be a part of our life.
Hayley and Craig said Archie's funeral will be a private service, adding: "If anyone would like to see Archie make his final journey to the crematorium we would love people to stand out on Churwell Hill to see him off at 12pm Wednesday November 24."
The couple said more than £70,000 was donated to a gofundme campaign for medical treatment that had been planned for Archie.
Donations of £5,000 each have been made to charities that helped the famly - Levi's Star Children's Brain Tumour Charity and Milly's Smiles.
Hayley and Craig said £60,000 has been used to set up charity ‘Archies Caravan’
They have bought a caravan on the Yorkshire coast for use by families with a child who has had a cancer diagnosis or is going through treatment.
A JustGiving appeal called 'Archie's Page' has been set up to raise funds for Candlelighters at www.justgiving.com/ArchieVaughan2017
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