He is said to be happy and in love with Ms Campion, his former staff member, and had taken personal leave before the baby's arrival.
Mr Joyce lost his cabinet position and the Nationals leadership after it was revealed he and Ms Campion were expecting a child.
Prime Minister Malcolm Turnbull later introduced a ban on ministers having sexual relations with their staff after the scandal unfolded.
Mr Joyce has stayed on as the member for New England on the back bench.
When he resigned, Mr Joyce said a "circuit-breaker" was needed to stop the fallout of his affair for his partner, for his unborn son, his four daughters, and estranged wife.
"This has got to stop. It's not fair on them," he said.
"I won't snipe. I have a lot of things I need to do.
"I want to assist my colleagues where I can to keep their seats and also, quite naturally, in April, a baby will be born.
"I'll have other things on my mind."
Mr Joyce also took a swipe at the media and any fellow MPs who had leaked against him for weeks before he was forced to step down.
"Over the last half a month, there has been a litany, litany of allegations," he said.
"I don't believe any of them have been sustained.
"Might I say right here, any person in any political party always says, the leaking, the backgrounding, all that, it will destroy not only our government, it will destroy any government."
Mr Joyce said he considered rural and regional Australians, the people in the "weatherboard and iron", when deciding to step down. He thanked his constituents for their support.
Mr Joyce was replaced by the Nationals new leader, and Deputy Prime Minister Michael McCormack.
In February, Mr Joyce and Ms Campion did their first sit-down interview, saying only God could judge him on his conduct.
They said they feared their baby son would be viewed "somehow less worthy than other children".
The couple claimed they had been "forced out" of their rent-free townhouse in Armidale due to media intrusion as they appealed to politicians and members of the public to give them privacy.
He insisted his working relationship with Mr Turnbull was fine and said that he had never directly asked him about the relationship with Ms Campion before it was revealed on the front page of The Daily Telegraph.
And even if the PM did ask him upfront, Mr Joyce admitted he probably would have lied. "(The Prime Minister) never asked any direct questions and to be honest, if I believed it was private, I wouldn't have told him either," Mr Joyce said.
Ms Campion said that her son's middle names would be in honour of her two brothers.
The affair led to Mr Turnbull and Mr Joyce having a public spat over the scandal.
Mr Turnbull held a press conference where he said Mr Joyce had made a "shocking error of judgment" that "appalled" everyone, as he changed ministerial standards.
Mr Joyce responds to Mr Turnbull's comments about his affair in an explosive press conference, saying they were "inept" and "unnecessary".
The pair held crisis talks in Sydney where they met for an hour in the Commonwealth Parliamentary Offices as they tried to work out their differences, until Mr Joyce decided to resign from his senior role in the Coalition.
