The bill - deemed the "heartbeat bill" - would ban abortions in Ohio from the moment a heartbeat can be detected.
This could be as early as six weeks into the woman's pregnancy.
The ban would make an exception if the woman's life was in danger but not in cases of rape or incest.
Lawmakers in the Republican-controlled state House voted to approve the bill on Tuesday night after it passed in the Senate earlier in the day.
The bill passed in the Senate with a vote of 21-10 and in the House with a vote of 56-39.
The state senate president Keith Faber said the bill had been brought back into consideration after Donald Trump's presidential success. The bill had previously been rejected twice.
The bill must now be signed or vetoed by Governor of Ohio John Kasich.
Gov Kasich is a pro-life supporter but has previously questioned whether the bill is constitutional.
Under the US Supreme Court's 1973 Roe vs. Wade ruling establishing a nationwide right to abortion, states were permitted to decide at what point the foetus could survive outside the womb.
Most US states ban abortion between 24 and 28 weeks of pregnancy.
Under current state law, abortion is illegal in Ohio after 20 weeks unless there is a risk to the mother's life.