The Human Tissues and Embryos Bill will give both women in a lesbian relationship the legal status of parents when one of them gives birth following fertility treatment.
This marks a historic change in how a family is legally defined.
The change was condemned by family campaigners as a "dangerous social experiment" but supporters said it was "'logical and just".
The bill says that where two women are in a relationship and one has fertility treatment to conceive then the partner should be treated as the other "parent".
In those circumstances no man - such as the sperm donor - can be treated as a father, the Bill says.