Ian Hislop said he was in disbelief that the Archbishop of Canterbury had the temerity to attend a lavish dinner after being forced out over his handling of abuse allegations against barrister John Smyth.
The Have I Got News For You star described it as 'jaw-dropping' that Dr Welby had showed up to the British Museum trustees' annual dinner last week after he had resigned in 'shame'.
In a column, Mr Hislop wrote: 'It was a gathering of the "great and good", but as I stood with a drink in my hand, I couldn't help noticing that the man standing across the Great Court from me was the Archbishop of Canterbury.
'This was the day after he had been forced to resign in disgrace for his role in an appalling scandal and cover-up of monstrous abuse in the Church of England.
'Like many guests there, I could not believe he would turn up to a public event. It was jaw-dropping.'
He said Mr Welby had approached his group and introduced himself, before looking around and asking, 'isn't this lovely?'
Mr Hislop added: 'I am afraid at this point I couldn't contain myself and refused to allow him to use the politeness of the British establishment to get away with what I thought was extraordinarily shameless behaviour.
'I said, "it is lovely that you have resigned."
Lambeth Palace said on Wednesday that Dr Welby intends to complete his official duties by January 6 and will have 'very little public-facing activity' between now and then.
His official functions will then be delegated to Archbishop of York Stephen Cottrell.
The BBC said Dr Welby will not deliver the traditional televised New Year message this year and it will return next year when a new Archbishop of Canterbury is appointed.
The Church has not confirmed whether he will deliver the Christmas Day sermon.