Yang Guang (Sunshine) and Tian Tian (Sweetie) were welcomed to Scotland to the sound of bagpipes as their "Panda Express" plane touched down at Edinburgh Airport.
The bears will spend 10 years on loan in the Scottish capital, a deal agreed after five years of high-level political and diplomatic negotiations.
Politicians are stressing their importance to relations between Britain and China, while Scotland is hoping for a tourism boost in austere times.
It is hoped the pandas will take advantage of a specially-built "tunnel of love" between their enclosures and breed new cubs that will help preserve the endangered species.
The bears were given an in-flight meal of bamboo, apples, carrots and a special "panda cake" on their journey from Chengdu in southwest China.
The duo were accompanied by two Chinese researchers who will help look after them until they adapt to their new life at Edinburgh Zoo.
On arrival at the airport, Tian Tian was the first to get a blast of the chilly Scottish weather, and could be seen checking out her new surroundings through her clear-sided box.
As dignitaries stood by on the tarmac, the pair were loaded onto trucks for the short journey to Edinburgh Zoo, where another bagpipe band dressed in kilts played traditional Scottish tunes to welcome them.
Locals waved Scottish flags, while some even dressed in panda outfits to cheer their arrival.
"As panda-mania hits Scotland, and we extend a warm Scottish welcome to Tian Tian and Yang Guang, I am delighted to have the opportunity to personally thank the Chinese government," said Scottish First Minister Alex Salmond, who is visiting China.
"The great gift of these giant pandas symbolises the great and growing relationship between Scotland and China."
The bears will spend a couple of weeks settling in before being put on public display, and Edinburgh Zoo has already reported a huge spike in ticket sales.
The zoo is paying about $1 million (750,000 euros) a year to the Chinese authorities for the pandas.
It has built two separate enclosures for the visitors, which are quite solitary, although they will be linked by the "tunnel of love" in anticipation of their hoped-for mating.
Each area contains an indoor section and a large outdoor enclosure, comprising lots of plants, trees, a pond and somewhere for them to shelter from the sun, a spokeswoman for the zoo said.
The pandas are expected to up to £70,000 ($110,000, 80,000 euros) worth of bamboo a year, with the zoo growing 15 percent and the rest imported from the Netherlands.
As of December 16, visitors to the zoo will be able to look in on the outdoor enclosure, while Internet users can follow Yang Guang on hidden "panda-cams".
Britain's Deputy Prime Minister Nick Clegg said the pandas' arrival was "a reflection of the strength of our relationship with China.
"It shows that we can co-operate closely not only on commerce, but on a broad range of environmental and cultural issues as well."
China is famed for its "panda diplomacy", using the endangered bears as diplomatic gifts to other countries.
Just 1,600 remain in the wild in China, with some 300 others in captivity.
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