Current rules limit the right to parents whose children are under six or disabled.
Following the recommendations of an independent review, John Hutton, the Business Secretary, said the move would give a "big boost" to busy parents.
But leaders of small businesses were less enthusiastic.
Andy Willox, OBE, Scottish policy convener of the Federation of Small Businesses in Scotland, said: "You can't have an extension of flexible working and at the same time clamp down on the means by which many small businesses cope with it, which is often through temporary workers."
David Lonsdale, assistant director of CBI Scotland said: "Extending the right to another four and a half million parents is a big step, and the government must give firms enough time to prepare, particularly smaller firms that lack the HR resource of bigger companies."
Flexible hours allow Shonagh McEwan, a Green Party researcher at Holyrood and her partner to juggle the care of their toddler son, Scott.
Ms McEwan, 31, from Edinburgh, who works 27 hours a week, said: "I'm still breastfeeding Scott, who will be two at the end of June. It is not one of those things you can rush."
She said her partner, Chris Ness, who works in the financial sector, is able to arrive and leave early when parliamentary business takes precedence.