Quicker divorce procedures, greater rights for unmarried fathers and measures to safeguard the interests of children have come into force.
Mr Henry said the reforms would increase protection for children
The Family Law (Scotland) Act is backed by a new helpline and website to give support and advice to families.
The Scottish Executive said the "radical" new law would protect children when relationships break down.
It comes as a Charter for Grandchildren has been launched, promoting the role grandparents play in children's lives.
The executive said the new Family Law Act would deliver seismic changes in the legal landscape, ensuring services and safeguards for "the way we live today".
Key provisions in the act include:
- establishing parental responsibilities and rights for unmarried fathers who jointly register the child's birth
- reducing separation periods for divorce without consent from five to two years and with consent from two years to one year
- legal safeguards for cohabiting couples to ensure the best interests of children are protected.
It is supported by the ParentLine Scotland helpline 0808 800 2222, which pulls together advice services and information for parents.
Further resources are being put online at the OK to Ask website.
Deputy Justice Minister Hugh Henry said: "Today modern laws come into force, laws which will make sure that the needs of children are not allowed to be forgotten when relationships break down.
"But legislative change is only part of the story. It needs to be backed by support services - available to all and easy to access."
Rachael Kelsey, chairwoman of the Family Law Association, welcomed many of the measures in the legislation.
Ms Kelsey said children could expect more equal treatment under the law now that unmarried couples could ensure parental responsibilities and rights.
She added: "Scotland is also the first part of the UK to give rights to cohabitants."
The Charter for Grandchildren, produced by the Grandparents Apart Self Help Group, has called for greater recognition of how grandparents fit into families.
It states: "Families come in all shapes and sizes. Grandparents, aunts, uncles and cousins can all play an important role in raising children.
"While parents are responsible for caring for their children and making sure their needs are met, the wider family can play a vital supporting role."