For the first time, couples who have children from a previous relationship will be able to have IVF treatment on the NHS.
The number of cycles women undergo will also be increased from two to three to increase the chances of success.
It is understood the changes to allow the treatment for couples who have a child living in their home could come in from September of this year.
The Scottish government will have talks with health boards about the possibility of allowing three cycles of IVF from April 2017.
One in seven couples will have difficulty having a child, and about 2% of births in the UK are now the result of fertility treatment.
Scotland’s health service has already met a target to see couples within a year and provide two rounds of treatment.
Public Health Minister Aileen Campbell said she hoped widening access to IVF would help more couples who were struggling to conceive.
She added: “Scotland already leads the way on IVF access and rights in UK, and these changes will ensure Scotland’s provision is a fair and generous as possible.”
She was responding to the publication of a report by the National Infertility Group, which had recommended the changes.
But Ms Campbell said the government would not be accepting a recommendation to remove eligibility for couples where the woman is aged between 40 and 42.
The existing criteria in this area would remain, Ms Campbell said, with women in that age range eligible for one cycle of treatment, if the couple fulfil certain additional criteria.
The National Fertility Group had said that successful outcomes for fertility treatment for women between 40 and 42 were “very poor”.
Prof Adam Balen, chairman of the British Fertility Society, said the announcement on the extension of IVF treatment was “great news for people in Scotland planning a family who have fertility problems”.
He added: “Infertility affects one in seven couples, and treatment should be available on the NHS. Infertility can have a devastating effect on people’s lives, causing distress, depression, and the breakdown of relationships.
“IVF treatment is cost-effective and enables childless couples the chance to have much wanted families.”
The society has pointed to a “gulf” between IVF funding in Scotland and England, saying there was still a “postcode lottery” for fertility services south of the border.