The state department has "issued the DSP-5 Guardian export license" for India, the source told PTI.
A DSP-5 category license is issued for permanent export of military hardware as found in the US Munitions List which is defined by the International Traffic Arms Regulations.
The Guardian drones will enhance India's maritime surveillance capabilities in the Indian Ocean region and their sale was announced by Trump on June 26 after he met Modi for their first face-to-face meeting.
The drones are estimated to cost around USD 2 billion and are being built by General Atomics, considered a pioneer in the unmanned aerial vehicles domain.
The speed with which the Trump administration decided on India's request for the drones, the source said, is reflective of the desire in White House to strengthen India's military capabilities in the Indo-Asia Pacific region, where China's aggressive diplomatic and military posture has unnerved other countries.
"We are extremely pleased that President Trump and Prime Minister Modi have had excellent deliberations and the path forward for a game-changer in US-India defence relations has been charted," said Vivek Lall of General Atomics.
Lall, who in his previous capacity at Boeing, was instrumental in the sale of high-tech military hardware to India, is believed to have played a role in convincing the Trump administration to accelerate the sale of the drones.
"Given the Sea Guardian's capabilities, such a response to the Indian Navy's request demonstrates a major change in US policy as this type of aircraft capability is only exported to a very select few of America's closest defence partners," he said.
"This represents tangible implementation of US Congress' designation of India as a 'Major Defence Partner'," said Lall.
On Tuesday, Lall met US Vice President Mike Pence on the sidelines of the annual US-India Business Council summit, when Pence endorsed the deal to provide India with Apache attack helicopters, C-17 transport aircraft, besides the drones.
The deal is seen as the biggest tangible takeaway from the Trump-Modi meeting towards the operationalisation of the major defence partner relationship.
The India Navy requested for the drones early last year.
But no tangible action was taken under the previous Obama administration, apparently because of the stiff opposition from the state department, which argued that this could upset Pakistan, America's ally in war against terror in Afghanistan.
The Trump White House spearheaded the inter-agency process to make a significant policy change in favour of India by granting this technology based on government-to-government interactions, the source told PTI.
India had been eyeing the Predator technology for years, and it was only the Trump-Modi combination that they were able to move the decision to this point, the source said.
Pakistan is said to be actively lobbying Washington against the sale of the drones to India. However, the White House overruled all objections, paving the way for a new phase of India-US defence relationship.