Monica Lennon’s member’s bill has won the backing of each of the five parties at Holyrood, giving her the right to press forward.
Her proposed Sanitary Products (Free Provision) (Scotland) Bill would create a statutory duty for free provision of sanitary products.
Ms Lennon said: “Scotland can lead the world on period poverty - and it is a positive step that all the parties at the Scottish Parliament have united behind these proposals.
“Access to sanitary products should be a basic right but sadly in Scotland we know not everyone can afford or obtain what they need.”
She added: “This bill would introduce a legal duty on the Scottish Government to develop a universal system in Scotland which will provide free sanitary products for anyone who needs them.
“There should also be a statutory duty on schools, colleges and universities to provide free sanitary products in their toilets. Having your period shouldn’t result in anyone missing class.
“This is bigger than party politics, this is about a fairer future for women and girls in Scotland. We can make that fairer future a reality.”
Consultation responses to the proposed legislation returned 96% supportive of the plans.
Equalities Secretary Angela Constance said: “In a society as rich as Scotland, no-one should have to suffer the indignity of not being able to meet their basic needs which is why we are already taking action.”
Referring to a pledge by Nicola Sturgeon in her programme for government unveiled in September, she added: “From autumn this year, we will be the first government in the world to fund access to free sanitary products in our schools, colleges and universities.”
Ms Constance said: “The Scottish Government wants to find the best way to support people in a sensitive and dignified way and we believe that we can best deliver this through working in partnership across the public, private and third sectors, building a consensus as to the best approach.”
A Scottish Government pilot scheme in Aberdeen to provide free sanitary products to those on low incomes has been extended while evaluation takes place.
A recent survey found more than two fifths of girls have used toilet roll to manage their period because they could not afford sanitary products.
The study by girls’ rights charity Plan International UK found 45% of respondents living in Scotland said they have been forced to use makeshift sanitary wear including socks or newspapers because they have struggled to buy products.