Some hope the Greek Orthodox Church will drop its opposition
The Greek Orthodox Church has until now opposed cremation, describing it as a violation of the human body.
The bill was passed by MPs after a campaign lasting almost 10 years.
The governing and main opposition parties all voted in favour of the bill, which means the country’s first crematoria can now be built.
But the law does not go as far as many involved in the long campaign would have liked.
In a compromise with the powerful Greek Orthodox Church, it will only apply to those whose religion allows cremation – in other words, the small minority of the population who are not Orthodox Christians.
But those behind the bill still describe it as a breakthrough.
They believe the Church will eventually drop its opposition to cremation for its own members if it becomes clear there is demand amongst the general population.
One member of parliament told the BBC that a window had now been opened. There are also strong practical reasons for allowing cremation in Greece.
The graveyards in the capital, Athens, are already full to overflowing. For many a burial plot is only rented for three years before the body has to be exhumed to make way for the next coffin.
It can be extremely distressing for relatives. Sometimes the exhumed bodies have not fully decomposed.