In his message, Delaney, 41, explained that Henry was diagnosed after suffering persistent vomiting and weight loss just after his first birthday.
The toddler underwent surgery to remove a tumour followed by further treatment throughout last year, spending 15 months in hospital. Sadly the cancer returned in the autumn and Henry died last month.
Delaney explained that while brain surgery left his son with "significant physical disabilities" he found his own ways to overcome them.
"He quickly learned sign language and developed his own method of getting from A to B shuffling on his beautiful little bum," said Delaney.
"His drive to live and to love and to connect was profound."
And the British-based American actor said he was determined to hold himself together, for the sake of Henry's grieving siblings.
"I am astonished by the love-in-action displayed by Henry's mom and his brothers. They are why I will endeavour to not go mad with grief.
"I don't want to miss out on their beautiful lives. I'm greedy for more experiences with them. The NHS nurses and doctors and the home carers and charity workers who helped our family survive Henry's illness will be my heroes until the day I die. I am desperately sad right now, but I can say with authority that there is good in this world."
I have very sad news. My two and a half year year old son Henry has passed away. Henry had been diagnosed with a brain...
Posted by Rob Delaney on Friday, 9 February 2018
And he ended his tribute with a message to his adored son.
"Thank you, beautiful Henry, for spending as much time with us as you did. We miss you so much."
Many celebs offered condolences on Twitter, including Paul Scheer, Rian Johnson, Amber Tamblyn and Jon Cryer.
Delaney first came to prominence on Twitter, sharing his jokes on the platform.
After developing a huge following, he was signed up to shoot a pilot for Comedy Central.
The show was not picked up, however Delaney went on to co-write and co-star in Catastrophe with Sharon Horgan, taking inspiration for the show from their own lives.
