The show, which will broadcast on BBC One and BBC Three, will follow each of the eight men from very different backgrounds over a 10-week period from late August.
Viewers will see the men on 'He's Having a Baby', which is being produced by Hat Trick, as they go into the delivery room and beyond.
During the programme, the dads-to-be will be put through a series of "dad assignments", which will give them first-hand experience of what lies ahead.
Leon Wilde, Hat Trick's head of entertainment and himself a new dad, said: "This isn't a 'how to parent' show. We're not trying to tell people how to be a dad, but are saying that it's cool to be a dad."
Each Saturday, McCall will catch up with the eight men live in studio to bring viewers their stories from the last week, which is likely to include tears before bedtime as the fathers struggle to change a nappy and try to juggle work and family.
"I really can't wait to do this programme, it's a well-known fact I'm evangelical about birth and I'm really looking forward to helping prepare these dads for the best journey of their lives," McCall said.
"Men largely get ignored when it comes to pregnancy, birth and becoming a parent, so it's time to give them a much-needed helping hand."
In addition to the BBC One coverage, BBC Three will capture their daily lives in what the BBC is describing as a real-life soap opera.
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