Savita Halappanavar was 31 when she died at University Hospital in Galway in October 2012.
Her husband Praveen had issued High Court proceedings against the HSE for negligence over her death.
The deal is thought to have significant financial implications for the HSE.
But details of the agreement have not been made public.
Proceedings were due to begin at the High Court on Friday, but the Irish state broadcaster RTÃ‰ has reported that the agreement was reached within the past few days.
Mrs Halappanavar had asked for a termination after being told she was having a miscarriage, but staff refused.
Days later, she died from infection.
The jury at the inquest into her death returned a verdict of medical misadventure.
Two subsequent reports into the circumstances of her death and the care she received at the hospital found several failings.
A report by the Health Information and Quality Authority found a failure to provide the most basic elements of care.
The 257-page report found that there were many missed opportunities, which, if acted on, might have changed the outcome for Mrs Halappanavar.
Praveen Halappanavar now lives in the US, having moved there in recent years for work.
The Republic of Ireland's Health Service Executive (HSE) is understood to have made an out-of-court settlement with the husband of a woman who died in hospital after a miscarriage.