But their new home, on another of the Marshall Islands, is struggling against huge tides and increasing storms.
The islanders have now asked Washington to change the terms of a trust fund to allow them settle in the US.
In 1946 several hundred islanders were moved from Bikini Atoll by the US government, which wanted to test atomic weapons on the remote atoll.
Some 23 nuclear tests were conducted including the huge Bravo hydrogen bomb, the largest weapon detonated at that time by the US.
The islanders moved to a nearby island in the Marshall chain called Kili in 1948.
Under an agreement with the US, a resettlement trust fund was eventually established to help the Bikini residents. This would pay for construction of homes within the Marshall Islands.
But now the islanders say that their homes are being swamped by the increased ingress of sea water during king tides.
There was widespread flooding in 2011 and again this year. Salt is also creeping up from beneath Kili, threatening agriculture and water supplies. In the early part of this year the island`s runway was entirely flooded, cutting off the residents.
"The people of Bikini came back to us and asked us to take this proposal to the US, to request the resettlement trust fund be used to settle people in the US not just the Marshall Islands," said Tony de Brum, Foreign Minister of the Marshall Islands.
"We have not seen the final text of the legislation but the request that went in was on the basis of Kili being uninhabitable because of climate change."
The US Department of the Interior is supporting the islanders and is now proposing legislation in Congress that would change the terms of the resettlement trust.
Under an agreement between the Marshalls and the US, islanders have the right to live, work and study in the US without restrictions on the duration of their stay.
"This is an appropriate course of action for the United States to take regarding the welfare and livelihood of the Bikinian people, given the deteriorating conditions on Kili and Ejit Islands in the Marshall Islands - with crowding,
diminishing resources, and increased frequency of flooding due to King Tides on their islands," said Assistant Secretary of the Interior Esther Kia`aina.
The Marshall Islands government says the experience of the Bikini islanders shows the need for a new global agreement on climate change.
They believe that a new deal can be agreed at a global conference in Paris that begins at the end of November.
One key element for the island state is that the agreement stipulate that global temperature rises be kept under 1.5 degrees C from pre industrial levels.
Minister de Brum said that from the point of view of small islands and atoll states, two degrees "cannot remain as the absolute cap for everything we are trying do in limiting global warming".
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