The agreement, signed on Tuesday during Trump's visit to the UN General Assembly in New York, stops short of Trump's demand that the US annex Greenland as a US territory to head off the growing Arctic presence of Russia and China.
But the deal does codify a greater US military presence on the icy territory, an option that emerged as Greenland leaders argued against a complete US takeover.
A text of the deal released after the event said the US can establish a "Golden Dome" defence system in Greenland as a shield against ballistic missile threats. The shortest route from Europe to North America runs via the Arctic island, which is the location of the northernmost US military base.
In his speech to the assembled world leaders at the UN before the signing ceremony, Trump said the agreement gives the US "permanent control over security and all other needs on that territory".
"No US adversary will ever be permitted to establish a military presence in Greenland any more, or make sensitive investments there without our express written approval," Trump said.
Trump signed the agreement along with Danish Prime Minister Mette Frederiksen and Greenland Prime Minister Jens-Frederik Nielsen in a trilateral ceremony after Trump gave his UN speech.
Frederiksen described the agreement as a deal that can "last forever" and said it underlines the importance of the NATO alliance and respects Greenland's right to self-determination.
Nielsen emphasised the importance of NATO in the Arctic region.
"We believe that it is vital to keep NATO strong, also in the Arctic, where the alliance has a key role to play," he said.
At a press conference after the signing, Nielsen said Greenlanders must now go through a process of restoring trust with the US. Trump's threats to take the island by force had strained relations with both Greenland and Denmark.
Greenland, a former colony and now a semi-autonomous territory of the Kingdom of Denmark, sits between the Arctic and North America and holds vast energy resources.
The US already operates Pituffik Space Base in remote northwestern Greenland. The deal opens two new military sites: Narsarsuaq, a former Cold War airbase whose population has dwindled to just a few dozen, and Mestersvig, currently used by the Sirius Dog Sled Patrol, a Danish special forces unit.
"We will immediately begin the process of developing a large military presence in the appropriate location. We will be building two very major military bases," Trump said in his UN speech.
Trump's refusal to rule out military or economic force to acquire Greenland triggered a diplomatic crisis in January within NATO and forced Denmark and the island's government into months of intensive negotiations.
The text of the agreement says it amends a 1951 defence treaty that had been the legal basis for the US presence.
It adds that Washington may seek further bases in the future, with details decided by mutual agreement. The deal has no end date, grants US aircraft and vessels broad access across Greenland and its territorial waters, and bars non-NATO states from establishing military installations on the island.
It also restricts foreign investment, effectively blocking states and investors from countries outside NATO, NATO partners and the European Union from holding control or significant influence in sectors deemed particularly sensitive, including critical infrastructure and resource extraction.
The deal, which needs approval by the parliaments of Denmark and Greenland, marks a shift from Trump's earlier ambitions for an outright acquisition of Greenland, an island three times the size of Texas with a population of only 57,000 scattered along its rugged coastline.
