The Health Service Executive's Saolta hospital group is offering almost 6,000 people the option of getting treatment in private hospitals, because of lengthy delays in the public health system.
The move comes after hospitals in the west and northwest failed to meet a Department of Health target to cut outpatient waiting times to less than 18 months.
Nationally, the HSE says around 20,000 people are being offered private appointments in a range of specialities.
It is estimated the private treatment will cost €25m.
In a memo to consultants, the Saolta group says all available outpatient capacity has been utilised to try to meet the deadline.
As this has not dealt with the issue, treatment is being outsourced to private healthcare providers.
As part of the arrangement, initial consultations, any required treatment and follow on appointments would all take place at private hospitals.
Patients were initially informed of the initiative by text message. These are being followed up with letters being posted out in the coming days.
Waiting times are most pronounced at Galway University Hospital, where 2,370 people have been waiting more than a year and a half for an outpatient appointment.
A total of 1,900 are waiting that long to see a consultant at Letterkenny General Hospital, with 770 on the list at Sligo Regional Hospital and 680 waiting for an appointment at Mayo General.
Fewer people are waiting past the 18 month time frame at the two other acute hospitals in the Saolta group – 200 in Roscommon and 22 at Portiuncula in Ballinasloe.
Latest figures from the National Treatment Purchase Fund show a further 9,000 people are waiting between 12 and 18 months for an outpatient appointment at one of the six hospitals in the group.
The HSE says improving waiting lists for scheduled care is a key objective for the health services in 2015.
At the start of the year Minister Leo Varadkar set the maximum permissible waiting time for inpatient, day case treatment and outpatient appointments at 18 months by 30 June.
He wants this reduced to 15 months by the end of the year.
The Executive says hitting these targets is challenging, due to issues such as consultant vacancies and theatre capacity.
While hospitals have been told to try to address the issue internally, the Health Service Executive says procedures are being outsourced through a public tendering process in order to ensure maximum permissible wait times are not breached.
Association launches plan for patient safety
Meanwhile, the Irish Patients' Association has launched a 'Pact for Patient Safety', which sets out ten commitments it would like health authorities to support.
The pact is already backed by 23 patient associations around Europe.
IPA director Stephen McMahon said the pact establishes key commitments for health authorities, such as providing full access to patient records, involving patients in patient safety programmes, publicising data on the issue and promoting safety with healthcare managers.
He said that patients, citizens and organisations everywhere can individually sign the pact and demand greater safety of care, through its website.
Minister for Health Leo Varadkar has said he will consider the recommendations closely in the efforts to reinforce safety standards here.
He has promised the establishment of a patient advocacy service, independent of the HSE.
The recommendation was made in the recent HIQA report into baby deaths at the Midland Regional Hospital Portlaoise.
That HIQA report said the service should be in place by May 2016, to ensure that patients' experiences are recorded, listened to and learned from.
At the pact launch, Ombudsman Peter Tyndall said that many complaints his office sees about healthcare could have been avoided, if the provider had properly responded to complaints they already received.
A Patient Safety Commission report was published in 2008, making 134 recommendations for safer care, including a licensing system for hospitals and other health facilities.