Sharing a picture of Henry as a baby on his Instagram, Delaney wrote in the caption: "This little boy would’ve turned 6 the other day.”
“He died of cancer a little bit before his third birthday.”
'If you asked me how I carry on without him I would tell you I don’t know.”
Delaney, 44 and wife Leah lost their son in January 2018, aged two, after he was diagnosed with a brain tumour.
Watch: Rob Delaney says his son’s death taught him to love his other children 'better'
Henry was diagnosed in 2016 after suffering persistent weight loss and vomiting shortly after his first birthday.
The infant spent 15 months in hospital undergoing surgery to remove the tumour alongside further treatment.
His family were told that his cancer had returned in the autumn of 2017 before he passed away in January 2018.
Later that year, in December, Delaney revealed that his wife had given birth to their ‘magical’ fourth son seven months after Henry’s passing.
The American actor has previously admitted on BBC Radio 4 that he is no longer afraid of dying and that it is his “staggering privilege to get to hold them [his sons], smell them and stare at them.”
He said: “Henry wasn't our only son and his death didn't make me love our other sons any less.”
“Because when I hold them, I know what they really are, they're temporary gatherings of stardust just like Henry.”
“I don't know if Henry's death made me love his brothers more, but it certainly made me love them better.”
Watch: Rob Delaney discusses his grief