It would allow for terminations on request for women who are up to 22 weeks pregnant.
After this time, terminations would be lawful if two doctors believe it should be performed in light of future physical, social and psychological circumstances.
The bill would also create a new criminal offence under the Crimes Act for those who assist in terminations who are not authorised to do so.
This would come with a maximum penalty of seven years in prison.
"The bill ensures women in NSW have access to safe and lawful terminations without the threat of criminal convictions and provides doctors with the legal clarity they have long sought," Mr Greenwich said in a statement on Sunday.
Based on laws already in place in Queensland and Victoria, the bill also has the support of the Australian Medical Association NSW.
It was developed by a cross-party working group including the National's Trevor Khan, and Labor's Penny Sharpe and Jo Haylen, with the oversight of Health Minister Brad Hazzard, who on Sunday welcomed the bill.
"Women in NSW should have the same reproductive rights as women in other states," Mr Hazzard said in a statement.
"This bill would ensure women and their doctors are appropriately protected in NSW and this medical procedure is properly regulated."
Liberals and Nationals MPs would be given a conscience vote if a private members bill was introduced to parliament to repeal the relevant sections of the Crimes Act, a NSW government spokesperson said in June.
The AMA said NSW was the last state in Australia to decriminalise abortion, placing women and doctors under a "different and stigmatised legal arrangement to other states".
The bill "reflects the common law entitlements that currently exist, while removing the stigma and legal uncertainty associated with abortion being included in the Crimes Act," AMA NSW said in a statement.
The NSW Pro-Choice Alliance also welcomed the bill, labelling laws which criminalise women and health workers as out of touch and irrelevant in modern society.
"It has been a long road, most significantly for women with unintended pregnancies but also for the health, legal, political and women's services who have fought long and hard to see this law overturned in recent decades," the alliance's chair Wendy McCarthy said in a statement.
Greens MP Jenny Leong congratulated those who had pushed for the reform.
"It's past time for women to have the right to make decisions about their own bodies. It's time for abortion law reform," Ms Leong said in a statement.
"If we succeed in getting this change through the NSW Parliament, it will be the culmination of a campaign that our mothers, indeed our grandmothers, feminists and pro-choice activists have been fighting for over generations."