The 41-year-old actor said his family were devastated following Henry's death in January in a statement on Facebook.
"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 tumour in 2016, shortly after his first birthday, following persistent vomiting and weight loss.
"He had surgery to remove the tumour and further treatment through the early part of 2017. Then the cancer returned last autumn and he died in January," Delaney said.
"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," Delaney said.
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"His tumour 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," he added.
"Thank you, beautiful Henry, for spending as much time with us as you did. We miss you so much," Delaney concluded the post.
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