"We're proud of Bristol's decision to have her baby and even prouder to become grandparents,'' Sarah and her husband, Todd Palin, said in a statement on Monday.
The news came as the Republican National Convention was to open in St Paul, Minnesota.
"Bristol and the young man she will marry are going to realise very quickly the difficulties of raising a child, which is why they will have the love and support of our entire family," the statement added.
The McCain campaign and the Palins have asked the media to respect the couple's privacy.
Steve Schmidt, a spokesman for McCain, said the Arizona senator considered the issue to be "a private family matter".
"As parents [the Palins] love their daughter unconditionally and are going to support their daughter. Life happens," he said.
Officials in McCain's election team said they were aware of Palin's daughter's pregnancy before they decided to pick her as the Arizona senator's running mate.
McCain officials said the news was being released to rebut "lies" circulating on the internet about Palin's children.
Rumours had been circulating on the internet that Palin had faked a pregnancy and pretended to have given birth in April to her fifth child, a son named Trig who has Down syndrome, when Trig was actually Bristol's child.
"There's no doubt that liberal blogs such as one called www.barackoblogger.com and some in the mainstream media were pushing a false story about Governor Palin's most recent pregnancy with fervour," said Nicolle Wallace, a senior McCain adviser.
A senior McCain official said its camp had no evidence that the campaign of Barack Obama, the Democratic presidential candidate, was pushing the story, but said the blog rumours circulating on websites that appeared to support Obama had the effect of being "a real anchor around the Democratic ticket".
Obama reaction
Obama called the news irrelevant and said candidates' children should be off limits in politics.
Speaking to reporters in Monroe, Michigan, Obama said he was offended by the McCain aide's statement.
"We don't go after people's families. We don't get them involved in the politics. It's not appropriate and it's not relevant. Our people were not involved in any way in this and they will not be. And if I ever thought there was somebody in my campaign that was involved in something like that, they'd be fired," Obama said.
"This shouldn't be part of our politics. It has no relevance to Governor Palin's performance as a governor or potential performance as a vice-president. So I would strongly urge people to back off these kinds of stories."
Palin is staunchly anti-abortion, and pro-life groups welcomed the decision to keep the child.
James Dobson, an influential Christian evangelical conservative, said the Palins "should be commended once again for not just talking about their pro-life and pro-family values, but living them out even in the midst of trying circumstances".
John Nichols, a writer for The Nation magazine, told Al Jazeera that among Christian evangelicals that form a significant part of the Republican party's base, Palin was likely to find a sympathetic response.
But, he said, the revelations could end up hurting McCain more than Palin as voters may fault McCain's judgment in his selection of Palin as running-mate.
The 44-year-old Palin, who opposes gun control and favours the death penalty, was announced on Friday as McCain's vice-presidential choice, drawing immediate criticism from Democrats that she was inexperienced.
Abuse of power probe
Also on Monday, it was revealed by the Alaskan legislature's investigative committee that Palin had hired a lawyer to represent her in a probe into whether she had abused her power in firing of a senior state official.
The Republican-dominated legislative committee is investigating whether Palin fired Walt Monegan, the public safety commissioner, after he refused to fire a state law enforcement official who had divorced Palin's sister.
Monegan was fired in July after he declined a transfer to become the director to the state's alcohol control board.
At the time Palin said she wanted the department to move in a new direction, but later, after Monegan said he felt pressed to fire Mike Wooten – Palin's former brother-in-law – by members of her administration, Palin said at a news conference that Monegan was not a team player, did not do enough to fill vacancies and battle alcohol abuse issues in rural Alaska.
State legislators say they want to know if the termination was personal rather than work-related.
Monegan has said he was never directly told by Palin or anyone to fire Wooten but that the governor, members of her administration and her husband, Todd, raised the issue about Wooten's employment numerous times.
Palin has steadfastly denied allegations of wrongdoing and has welcomed the investigation, saying "hold me accountable".