The law came into force after a referendum in February which was ruled invalid because of low turnout but indicated that 59.25 per cent wanted to lift the ban.
That led the ruling Socialists, with a majority in parliament, to legalise abortion.
The referendum campaign pitted the urban young against people from traditional rural areas and the Catholic Church.
Women who choose to abort will have to go through a compulsory medical appointment to be properly informed about the consequences of abortion.
The government hopes the new law will reduce an estimated 23,000 clandestine abortions every year.
Local media reported that at least nine regional hospitals in Portugal will not carry out abortions because doctors there object to them.
In Europe, Malta, Ireland and Poland still have highly restrictive abortion laws.