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It means mixed-sex partners will have the same choices of marriage or civil partnerships as same-sex couples.
The bill came about after a Supreme Court ruling which found that the existing UK law went against the European Convention on Human Rights.
Civil partnerships were first made available to same-sex couples in 2005.
Last year, the Scottish government consulted on two options following the ruling – whether to extend civil partnerships or to scrap them.
After considering all 481 responses, ministers decided to make the partnerships – which offer the same legal and financial protection as marriage – available to everyone.
Social Security Secretary Shirley-Anne Somerville said the legislation would allow all couples to make the same choices.
She said: “Fundamentally, extending civil partnerships to mixed-sex couples is about equality, fairness and choice.
“This bill means all couples will have the same choices if they decide they want to make a lasting commitment to each other through a legally-recognised relationship.
“Just like same-sex couples, mixed-sex couples will be able to choose to enter into a civil partnership if they feel this is right for them.”