Minister for Justice Helen McEntee has announced that direct provision residents in the Skellig Star Hotel in Cahersiveen in Co Kerry will be relocated over the coming weeks and months.
Speaking in the Seanad, she said places for the first families are currently being identified and moves for them will be completed by the end of next week.
The minister confirmed that other residents in the centre will be moved to permanent accommodation as soon as spaces can be found.
She said this would be completed in no more than a few months.
Minister McEntee said when a group of people feel they need to put their health at risk by refusing food, she was forced to listen to their concerns.
She said she appreciated that the Covid-19 outbreak in the centre was extremely distressing for residents.
The minister said restrictions on transfers that were necessary as a precaution during the pandemic have now been relaxed.
She said the Government's policy is always to withdraw from emergency accommodation as quickly as possible and that this will now be implemented in relation to Cahersiveen.
She also told the Seanad that the replacement of the direct provision system more generally will not happen overnight and existing centres will continue to operate in the short to medium term.
They have been demanding to be moved to other direct provision centres elsewhere in the country.
Sinn Féin Spokesperson on Equality, Inclusion and Law Reform Pa Daly this evening said he welcomed the decision of residents to end their hunger strike.
In a statement, he said: "I know from dealing with the residents of the Skellig Star in recent months that going on hunger strike was not a decision they took lightly."
He added: "I am glad that the Minister for Justice has taken their concerns on board and has announced today that residents will be relocated over the coming weeks.
"This should happen sooner rather than later, and the residents must be moved to suitable accommodation which is sensitive and appropriate to their needs."
Solidarity-People Before Profit TD Brid Smith said the 32 people had been facing their third day on hunger strike in the hotel, saying they had taken a "pretty drastic" decision to highlight their situation in direct provision.
Speaking in the Dáil, she raised their living conditions and said they would "do better in a refugee camp in the Lebanon".
Ms Smith said the residents need to be moved out, to own-door accommodation in Tullamore or Mosney.
The centre is located at the former Skellig Star boutique hotel and was opened in mid-March, when over 100 residents were moved there.
The first cases of coronavirus among residents were confirmed in early April, just over a fortnight after the centre opened.
Calls for its closure were made both by residents of the centre and by local people.
They claimed the centre was not fit for purpose, and social distancing was impossible there. Since then there have been around 20 cases of coronavirus among residents.
In May, then justice minister Charlie Flanagan apologised to the people of Cahersiveen for the manner in which the direct provision centre was opened there. However, he rejected calls for it to be closed.
On Tuesday, a spokesperson for the residents said that 28 people began refusing food that morning in protest at conditions in the centre.