The solar-powered craft completed two weeks of non-stop flight above a US Army range in Arizona before being commanded to make a landing.
The Qinetiq company which developed Zephyr said the UAV had nothing to prove by staying in the air any longer.
It had already smashed all endurance records for an unpiloted vehicle before it touched down on Friday.
"We are just really delighted with the performance," said project manager Jon Saltmarsh.
"It's the culmination of a lot of years of effort from a huge number of really talented scientists and engineers," he told BBC News.
Zephyr took off from the Yuma Proving Ground on Friday, 9 July.
After only 31 hours in the air, it had bettered the official world record for a long-duration flight by a drone; but then it kept on going, unencumbered by the need to take on the liquid fuel that sustains traditional aircraft.
Clear skies at 60,000ft delivered copious amounts of sunshine to its amorphous silicon solar arrays, charging its lithium-sulphur batteries and keeping its two propellers turning.
At night, Zephyr lost some altitude but the energy stored in the batteries was more than sufficient to maintain the plane in the air.
Zephyr is set to be credited with a new world endurance record (336 hours, 24 minutes) for an unmanned, un-refuelled aircraft - provided a representative of the world air sports federation, who was present at Yuma, is satisfied its rules have been followed properly.
Its fortnight in the sky easily beats the 30 hours, 24 minutes, set by Northrop Grumman's RQ-4A Global Hawk in 2001.
Zephyr has also exceeded the mark set for a manned, non-stop, un-refuelled flight, set in 1986 by Dick Rutan and Jeana Yeager, who stayed aloft for nine days (216 hours), three minutes. Their flight in the Voyager craft went around the world.
Jon Saltmarsh said the UAV, which has a 22.5m wingspan, was no longer an experimental plane and was now ready to begin its operational life.
The fact that Zephyr completed its demonstration during the Farnborough International Airshow - which takes place on the doorstep of the Qinetiq company - will have done wonders for the craft's profile.
Solar-powered high-altitude long-endurance (Hale) UAVs are expected to have a wide range of applications.
The military will want to use them as reconnaissance and communications platforms. Civilian and scientific programmes will equip them with small payloads for Earth observation duties.
Their unique selling point is their persistence over a location. Low-Earth orbiting satellites come and go in a swift pass overhead, and the bigger drones now operated by the military still need to return to base at regular intervals for refuelling.
"Qinetiq is now looking to the Ministry of Defence and the DoD (US Department of Defense) to put a system into service," said Mr Saltmarsh.
"We have proved the concept; we have proved we can provide persistence; we have proved we can put useful payloads on to it that will actually do things the MoD has a requirement to do."
The Zephyr flight is the second event of note this year in solar-powered aviation. Earlier this month, Andre Borschberg became the first person to pilot a manned solar plane through the night.