Migrants are being transferred from Bibby Stockholm and to hotels across the country, with reports suggesting that between 300 and 400 will be relocated.
Once they have been placed in temporary accommodation, they will be told if they can stay in the UK.
The government is releasing the migrants from the ship before the contract to use it expires in January.
Labor has said it will not resume the use of the Bibby, which is docked off Portland, after that date as the Home Office expects demand for such accommodation to be reduced by action to clear the backlog of asylum applications.
The vessel was one of several sites, including RAF Wethersfield in Essex and RAF Scampton in Lincolnshire, used by the previous Tory government in a bid to reduce the cost of housing migrants in hotels.
But Labor said continuing to use Bibby Stockholm would cost more than £20m next year and scrapping it was part of an expected £7.7bn saving in asylum costs over the next 10 years.
The asylum seekers housed on the barge, who are all men, are spread out in places including Cardiff, Wolverhampton and Bristol, according to the BBC.
None of these will be moved into Dorset Council’s catchment area, which includes the area around Portland and Weymouth.
A Home Office spokesman said: “This Government has inherited an asylum system under unprecedented pressure, with thousands left in a backlog without their claims being processed.
“We have taken immediate action to restart asylum processing, which will save the taxpayer around £7 billion over the next 10 years, and we are delivering a significant increase in returns to remove people without a right to be in the UK. In the long run, this will reduce our dependence on hotels and accommodation costs.
“We remain absolutely committed to ending the use of hotels for asylum seekers.”