Charles Kennedy and his wife Sarah have spoken of their "absolute delight" after the birth of their son.
Sarah Kennedy supported the Lib Dem campaign on Sunday
Mrs Kennedy gave birth to Donald James, who weighed six pounds, nine ounces, at 0014 BST at St Thomas' hospital, London. Both are said to be doing well.
Tony Blair and Tory leader Michael Howard were quick to offer their congratulations to their colleague.
The party had been due to launch its manifesto but that was postponed after Mrs Kennedy entered hospital on Monday.
The couple and their baby are expected to leave hospital later on Tuesday.
Labour leader Tony Blair said: "I just wish them well and we all wish them well. It is a particular joy when you have your first baby."
For the Tories, Michael Howard said: "It is wonderful news. I send them my warmest congratulations."
In their statement Mr and Mrs Kennedy said: "It is wonderful for us both and we are extremely grateful for the superb clinical and midwifery support which we have received."
Recalled to London
They added: "Everything went very smoothly and we are looking forward to returning home as a family in due course."
It has been reported that the baby is named after Mr Kennedy's grandfather Donald, to whom the leader was very close.
Deputy leader Sir Menzies Campbell has taken over Mr Kennedy's campaign duties while the Lib Dem leader stays with his wife and new son.
Mr Kennedy had been due to board a plane for Devon on Monday but was called back to London after his wife, 35, was admitted to hospital.
Mrs Kennedy appeared alongside her husband on the campaign trail for the first time on Sunday.
The Liberal Democrats held a news conference about the economy on Tuesday and Sir Menzies took Mr Kennedy's place on a visit to Bristol.
Lib Dem campaign chief Lord Razzall told journalists: "We are all absolutely delighted and send our congratulations to Charles and to Sarah.
"Charles will be rejoining the campaign shortly."
The Lib Dem trade and industry spokesman Malcolm Bruce told BBC News: "It will do the campaign absolutely no harm.
"It's not just women - an awful lot of men like babies too and people generally respond warmly to family pictures.
"It makes a point that here is a man who has a new family and I think a lot of the issues we are addressing are about families in Britain today.
"We are happy for any family that has an event of this kind and it is just one of those fortuitous outcomes that Charles and Sarah have had a baby at the start of an election campaign."
Sir Menzies told BBC News he would be fulfilling Mr Kennedy's engagements "for the next day or two".
"This is a contingency we had allowed for in our planning for the general election and I think we have simply taken that particular file out of the drawer," he said.
Sir Menzies said the party's campaign had always been a team effort, adding: "It does not mean Charles is out of the election altogether.
"He will obviously continue to take a part, give advice and participate in those parts of the election campaign and its planning that do not require him to leave the bedside of his wife."
Speaking to Radio 1's Newsbeat shortly before hearing his wife had been admitted to hospital, Mr Kennedy said he was "very nervous, apprehensive, excited" about the birth.
When asked if he was looking forward to changing nappies, he said: "I dare say that will do me good, I've been getting some theoretical demonstrations of this with Sarah, my wife, already.
"There's an altogether new man you've got sitting here."
He also told GMTV: "The priority for an interlude will be Sarah and the baby but I will not be forgetting my day job."