The park at Branton, near Doncaster, came to the rescue after a museum on the Japanese island of Hokkaido announced it lacked the experience or resources to look after the bears properly.
Riku, Kai, Hanako and Amu, as the bears are known, will become the first residents of a new 2.5km rehabilitation centre at the park, which is calling for volunteers to help create new features in the reserve ahead of their imminent arrival.
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Ussuri brown bears, whose natural habitat is the forest, weigh up to 550kg and can live for up to 35 years.
They are a threatened species, which are vulnerable to poachers and have become extinct in parts of Asia, and there are thought to be only 10,000 remaining in Japan.
The bears are due to arrive soon and the park said a plan is being put together to guarantee their safety on the 5,400-mile journey.
They will become the first residents of a new rehabilitation centre at the park, where bosses have called for volunteers to help create new features to make them feel at home in the 2.5-acre specialist reserve where they will be housed initially.
The park teamed up with the UK charity Wild Welfare to organise the move.
Georgina Groves, the charity's projects director, said: "It's great that these four bears are coming to Yorkshire Wildlife Park, which has a great track record.
"We know they will provide the bears with a great home, where they can receive the rehabilitation, enrichment and life-long care they need."