"We're going to check out how things are going there," Vance said in a video shared on Tuesday.
"Speaking for President Trump, we want to reinvigorate the security of the people of Greenland because we think it's important to protecting the security of the entire world."
President Donald Trump irked much of Europe by suggesting that the United States should in some form control the self-governing, mineral-rich territory of American ally Denmark.
Greenland has broader strategic value as both China and Russia also seek access to its waterways and the nearby natural resources.
The vice-president's decision to visit a US military base in Greenland on Friday has removed the risk of violating potential diplomatic taboos by sending a delegation to another country without an official invitation.
Yet Vance has also criticised European allies for relying on US military support, openly antagonising partners in ways that have caused concern about America's reliability.
Before the vice-president's announcement that he would join his wife, discontent from the governments of Greenland and Denmark had been growing sharper, with the Greenland government posting on Facebook on Monday night that it had "not extended any invitations for any visits, neither private nor official".
Danish Prime Minister Mette Frederiksen said the visit was "unacceptable pressure", and Greenland's acting head of government, Mute Egede, labelled it a "provocation".
The office of second lady Usha Vance said on Sunday that she would depart on Thursday for Greenland and return on Saturday.
Vance and one of her three children had planned to visit Greenland's historical sites, but her husband's participation has reoriented the trip around national security.
He plans to visit a Space Force outpost on the northwest coast.
Vance said leaders in Denmark and North America had "ignored" Greenland for "far too long".
Trump's national security adviser, Mike Waltz, was initially listed among the group of US officials also heading to Greenland, but his name was omitted when it was announced that the vice- president was attending.
The White House did not say if Waltz's travel plans had been altered after it was revealed he had errantly added a journalist to a secure messaging app conversation about a military strike in Yemen.
During his first term, Trump floated the idea of buying the world's largest island, even as Denmark, a NATO ally, insisted it was not for sale and the people of Greenland also firmly rejected the plan.
Trump's return to the White House has included a desire with territorial expansion, with the US president seeking to add Canada as a 51st state and resume control of the Panama Canal.
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