The decision comes after a huge public outcry over the death of the 31-year-old, who died on October 28 at Galway University Hospital. She had been 17-week pregnant and was found to be miscarrying.
Savita's husband said she asked repeatedly for a termination of the pregnancy but was refused and was told the foetal heartbeat was still present and "this is a Catholic country".
The Irish government has decided to repeal legislation that makes abortion a criminal act and to introduce regulations setting out when doctors can perform an abortion when a woman's life is regarded as being at risk, including by suicide, the Telegraph newspaper reported.
Irish health minister Dr James Reilly said that the government was aware of the controversy surrounding abortion.
"I know that most people have personal views on this matter. However, the government is committed to ensuring that the safety of pregnant women in Ireland is maintained and strengthened. We must fulfil our duty of care towards them," the paper quoted Dr Reilly as saying.
"For that purpose, we will clarify in legislation and regulation what is available by way of treatment to a woman when a pregnancy gives rise to a threat to a woman's life. We will also clarify what is legal for the professionals who must provide that care while at all times taking full account of the equal right to life of the unborn child."
Irish Prime Minister Enda Kenny said the draft legislation would be published in the New Year with a timetable of having the legislation ready by Easter.
To ensure the law is passed the government whip would be applied to MPs in the ruling Fine Gael party which is deeply divided over the proposals, the paper said.
"There will be no free vote on this," Kenny said. Under current Irish law abortion is criminal unless it occurs as the result of a medical intervention performed to save the life of the mother.
The Irish cabinet's decision follows pressure from the European Court of human rights, which ruled that abortions should be allowed in cases where a woman's life was at risk.
Ireland's abortion laws are the strictest in Europe and any proposed legislation to decriminalise abortion will stoke furious debate in the country, which remains a staunchly Roman Catholic country.