Nick Clegg will demand a culture change across British industry to tackle "old-fashioned attitudes" to flexible, family-friendly working practices.
The Deputy Prime Minister will say that despite efforts to introduce flexible parental leave and extend free childcare there are "hidden prejudices" which can limit women's career ambitions and men's ability to spend time with their families.
He will urge parents and teachers to inspire girls to focus on high-flying careers and insist that countries such as Switzerland, Sweden and the Netherlands have shown that it is possible to have family-friendly working conditions while remaining competitive.
In a speech at the launch of Cityfathers, a network for working dads in the City of London, Mr Clegg will say that "radical change" is needed, including sweeping away the "Edwardian rules" which hold back working families.
Mr Clegg will say how he "fought to drag those clapped out rules into the 21st century".
As well as measures to improve access to childcare, including the tax break worth up to £2,000 due to come into effect next autumn, Mr Clegg will highlight the changes allowing fathers to share parental leave from April next year.
But he will say that changes to the law are "only the start" and "culturally, we also need to recognise that we can't build a more family-friendly Britain unless all of us see the world differently".
Mr Clegg will say: "We need to tackle once and for all the hidden prejudices which still limit the choices of many men and women. And we need to create the same equal opportunities for both sexes to care as well as earn.
"How do we do that? Well, we've got to tear down those barriers which still prevent too many brilliant women from reaching the top of their professions.
"For example, despite progress in recent years, women still account for just 21% of board positions on FTSE 100 companies. And only four of those companies have a female CEO.
"That impacts on all of us, with estimates showing that the UK could boost its GDP by up to £23 billion if we use the skills of our female workforce more effectively.
"Parents and teachers have an incredibly important role to play here: inspiring every young girl to think big and aim high for their future. If they've got the talent and ambition to succeed, then no job should be closed off to them - whether it's to build their own business, lead a top company or work at the cutting edge of science, technology or engineering."
More also needs to be done to encourage men into caring professions, Mr Clegg will say, with people making choices "based on what's right for them not outdated preconceptions about their gender".
He will say many fathers are "pushed to see themselves as a breadwinner first and carer second" and around a quarter of new fathers take only a week or less of paternity leave.
Mr Clegg will say that some City firms had already recognised the benefits of a better work-life balance.
" Yet that kind of fantastic corporate support still isn't translating into the wholesale shift in attitudes we need," he will say."That's especially true in jobs with an entrenched long hours' culture like here in the City."
He will urge business leaders to ensure every family who can benefit from the new rights is able to do so, adding that " together we can generate a once-in-a-generation chain reaction across our offices, factories and other workplaces".
He will say: " As competition increases, no successful business leader would think twice about investing in the latest technology to help their business get ahead. In the same way, we need to show how an upgrade in old-fashioned attitudes to flexible working can sharpen competitiveness even more."
Parenting charity NCT's chief executive Belinda Phipps said: "We welcome the focus the Government has placed on this issue and we're pleased to see a spotlight on the need for better equality in the workplace.
"It's shocking that so few fathers currently feel able to take advantage of paternity leave. One of the problems behind this is the low level of statutory maternity and paternity pay - less than the weekly national minimum wage.
"NCT would like to see the Government take action to increase maternity and paternity pay and ensure fathers can afford to take advantage of shared parental leave when it comes into effect."