The Government had pledged to provide up to 1,000 homes for rough sleepers and single people in emergency accommodation.
The scheme is being run under the Housing First model which allows homeless people to move directly into permanent accommodation.
All local authorities around the country have signed up to providing their share of the extra homes under Housing First.
It will also involve homeless people being settled in rural areas.
There are currently 214 Housing First units occupied, the Government has pledged another 663, with plans for more while it is hoped to have 75 ex-prisoners also housed under the scheme,
Launching the scheme, Minister for Housing Eoghan Murphy TD said it had an 85% success rate, with the vast majority of tenants staying in their new homes.
National director of Housing First Bob Jordan said that each tenant has support services who can liaise with local communities.
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Meanwhile, Father Peter McVerry has expressed concern over the Government's housing strategy.
Speaking at a Solidarity press conference this morning, Fr McVerry questioned if the Government were "more concerned with the housing crisis at the top of the market than they were with the housing crisis at the bottom of the market".
Fr McVerry said there were two types of housing crisis - one was a social housing problem, affecting low-income families, while the other affected people on good salaries at the top of the market, who could not afford to buy a home.
He echoed calls from the Solidarity Party this morning for "public homes on public lands".
Fr McVerry warned that "we are never going to solve the social housing crisis by giving public land to private developers in return for thirty, or twenty or even ten percent social housing".
He also criticised Government for being overly concerned about creating "mono-class estates", in which social houses would make up a significant amount of the total number of homes.
Fr McVerry said he believes that problems associated with such developments are largely due to a lack of services and facilities to cater for the community.
Solidarity claim that NAMA and local authority land has the potential to deliver 114,000 public homes.
Their housing spokesperson, Mick Barry, said the party would advocate for 100% social and affordable housing.
When asked who would build these homes, Solidarity Councillor Michael O'Brien said that building companies would be hired by local authorities.
The party is also calling for a change in income eligibility for affordable housing. Solidarity believe that affordable houses should cost less than €200,000.
This afternoon, Cork's Housing Action Group is ostaging another 24-hour protest outside Leinster House again today, calling for the setup of a National Emergency Committee on Housing & Homelessness.
This is the 10th such protest, at a time when housing lists are longer than ever and families are facing desperation.
Rents in housing are at an all-time high, Rogue Landlords are allowed to extract rack rents and evict at will.
The group is calling on all candidates in the Presidential Election to declare their position on homelessness.
Additional reporting: Tommy Meskill and Paschal Sheehy