The refugees have been offered new lives in the United States and other nations after the failure of years of negotiations to secure their return to Bhutan, which says they are illegal immigrants.
Less than 18,000 refugees remain in the camps, according to a joint statement from the UN Refugee Agency (UNHCR) and the International Organization for Migration.
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All are ethnic Nepalese who fled across the border in the early 1990s, claiming persecution after Bhutan made national dress compulsory and banned the Nepalese language.
"This is one of the largest and most successful programmes of its kind and the resettlement of nearly nine out of 10 Bhutanese refugees is an extraordinary achievement," said Craig Sanders, the UNHCR's representative in Nepal.
The programme began in 2007 following the failure of years of high-level negotiations to secure their return to Bhutan.
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More than 84,000 refugees have left for the US, while Australia, Canada, Denmark, New Zealand, the Netherlands, Norway, Denmark and Britain have also taken thousands.
Refugee Devi Maya Thapa Thapa will head to the US with her family next month, becoming the 100,000th Bhutanese to be resettled.
"I am leaving the refugee camp forever after spending more than two decades in Nepal. I am happy that our family will be together in our new country and that my children will have a better future," the 55-year-old said in the statement.
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