The agreement, expected to be signed at the UN General Assembly in New York on Tuesday, has not been made public, though President Donald Trump says it grants the US "permanent control".
Denmark and Greenland have not commented on Trump's claim but said the deal will benefit the Arctic island and respect its sovereignty.
The deal follows months of pressure from Trump, who has said the United States should control Greenland and at times refused to rule out using military or economic force to acquire the semi-autonomous Danish territory.
Trump's threats, which peaked in January, triggered a diplomatic crisis within NATO and pushed Denmark and Greenland into negotiations with Washington aimed at defusing the pressure.
"It (the agreement) will be in a form where responsibility for security in the Arctic is not only Danish or American," Danish Foreign Minister Lars Lokke Rasmussen told national broadcaster TV2.
He added that to a large extent "it would be NATO that looks after the Arctic".
A NATO spokesperson said the alliance welcomed the agreement, which would "help advance security, stability and co-operation in this vital region".
Rasmussen, who travelled to New York overnight, declined to discuss the contents of the agreement.
"But we have said from the start that we are open to accommodating the United States' legitimate security interests," Rasmussen told Danish news agency Ritzau.
Trump said in a post on Truth Social on Friday the agreement gives the United States "permanent control over security, and all other needs, in Greenland," and that no US adversary could have a base or military presence there without Washington's written approval.
Denmark has not responded to Trump's claim, though Copenhagen has earlier acknowledged it underinvested in Greenland's defence for decades and has pledged to expand its military presence on the island, including more NATO troops.
Key details have not been made public, including whether the deal amends the 1951 defence agreement that is the legal basis for the US presence in Greenland.
Greenland's government has sought to reassure the public about the deal.
Erik Jensen, an opposition politician in Greenland, wrote on Facebook that he had read the draft agreement: "I feel reassured and am not worried," he said.
