More than 2,500 women may seek a medical abortion from a GP or maternity hospital next year.
The figure is based on the number of early terminations recorded by UK clinics last year among women who travelled from the Republic of Ireland.
The Regulation of Termination of Pregnancy Bill, which concluded its passage through the Oireachtas on Thursday night, is due to go to President Michael D Higgins to be signed into law next week.
He has five to seven days to consider the legislation, which Health Minister Simon Harris wants to have in operation from January 1.
It will be the second week of January before any medical abortions, up to 12 weeks of pregnancy, will take place in GP surgeries or maternity hospitals because of the three-day rule that must be observed.
The HSE is to begin widely publicising the 'My Options' helpline once the legislation is enacted.
This will give information on counselling, as well as details of the nearest participating GP.
Banner digital ads will appear on websites to inform women of the helpline, which will also be the subject of a radio campaign.
From the middle of January, the number will be appearing on bus shelters and female washrooms in pubs, clubs and colleges.
The HSE said yesterday it continues to get a "steady return" of application forms from GPs who will participate in the scheme.
Clinical guidelines are due to be distributed to doctors and hospitals next week on the optimum care and safety of women who seek the treatment.
Many GPs will hold out and not participate until all systems relating to termination services are up and running.
A significant number of GPs, who have conscientious objections to performing abortions, will also refuse to refer a woman and the impact of this has yet to be seen.
Mr Harris insisted yesterday that doctors who want access to ultrasound will have it through private providers or additional services from maternity hospitals.
Women seeking late abortions - who do not fall into categories covered in the legislation - will still have to go to the UK for terminations.
Last year, some 519 Irish women had later abortions, including 118 at 20 weeks of pregnancy or beyond.
It is unclear how many of these involved women whose unborn child had been diagnosed with a fatal foetal abnormality.
These women will now be entitled to a termination in Ireland under the new law.
Orla O'Connor, of the National Women's Council, said: "While recognising that this legislation does not do everything we have advocated for, such as decriminalise abortion and allow for safety zones to protect women from protesters, the act will give effect to the enormous public mandate that the Yes vote on May 25 gave us."