The actor shared an emotional statement on Facebook, in which he said he would “endeavour not to go mad with grief”.
Rob told of how Henry passed away in January, after his cancer returned last autumn.
He’d previously had surgery to remove a brain tumour at the age of one, which left him with physical disablities.
“I have very sad news. My two and a half year old son Henry has passed away,” he wrote.
“Henry had been diagnosed with a brain tumor in 2016, shortly after his first birthday, following persistent vomiting and weight loss. He had surgery to remove the tumor and further treatment through the early part of 2017. Then the cancer returned last autumn and he died in January.”
He continued: “My wife and Henry’s older brothers and I are devastated of course. Henry was a joy. He was smart, funny, and mischievous and we had so many wonderful adventures together, particularly after he’d moved home following fifteen months living in hospitals.
“His tumor and surgery left him with significant physical disabilities, but he quickly learned sign language and developed his own method of getting from A to B shuffling on his beautiful little bum. His drive to live and to love and to connect was profound.
“I am astonished by the love-in-action displayed by Henry’s mom and his brothers. They are why I will endeavor 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.”
Rob went on to pay tribute to hospital staff who had cared for Henry.
“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,” he said.
“I am desperately sad right now, but I can say with authority that there is good in this world.”
Rob asked fans to donate to Rainbow Trust (https://rainbowtrust.org.uk) or Noah’s Ark (https://www.noahsarkhospice.org.uk) in his son’s name, saying his family would be “in much worse shape right now if it weren’t for them”.
He also asked for privacy saying he “nothing else to say that I haven’t said here”.
“Thank you, beautiful Henry, for spending as much time with us as you did. We miss you so much,” he added.