Parents will be offered a flexi-time arrangement for leave from work after the birth of a new baby.
The plan will move Britain away from an "Edwardian" system that causes suffering to women, men and children, Mr Clegg said.
He made the announcement at the launch of a report by think-tank Demos, which has warned that overwork, stress and inflexible hours are undermining parents' confidence in their ability to bring up children.
Under plans drawn up during the last Labour Government, fathers will be able to take up remaining unpaid maternity leave if mothers decide to go back to work early, for a maximum of six months.
"Too many of these parents feel trapped by the current, rigid rules. We want to give them the flexibility that sets them free," he said.
Current rules allow men a "paltry" two weeks of paternity leave - and "patronise women and marginalise men", according to Mr Clegg.
Mr Clegg says current rules 'patronise women and marginalise men'
"They're based on a view of life in which mothers stay at home and fathers are the only breadwinners. That's an Edwardian system that has no place in 21st century Britain.
"Women suffer. Mothers are expected to take on the vast bulk of childcare themselves. If they don't, they very often feel judged. If they do, they worry about being penalised at work," he said.
"Children suffer, too often missing out on time with their fathers - time that is desperately important to their development.
"We know that where fathers are involved in their children's lives they develop better friendships, they learn to empathise, they have higher self-esteem, and they achieve better at school.
"And men suffer too. More and more fathers want to play a hands-on role with their young children. But too many feel that they can't. It's madness that we are denying them that chance. That culture must change."
David Frost from the British Chambers of Commerce told Sky's Boulton And Co programme he was concerned "short term chunks" would be tough for employers. "How do businesses get the cover and plan for the future?" he asked.
"Is this going to create jobs or harm job creation? Our view is it is absolutely going to hit it."
Other business leaders have described the plans as "a complete nightmare" with employment law barrister Daniel Barnett telling Sky News: "It sounds noble, but is deeply impractical...it will have a chilling impact on recruitment practice.
"Many employers shy away from hiring women of childbearing age. Nick Clegg's proposals might see employers avoiding recruitment of any person in their 20s or 30s, which would lead to an increase in the number of age discrimination claims and the burden of tribunal claims on employers."
Yvette Cooper, shadow equalities minister, said Labour had increased and extended maternity leave, introduced time off for fathers and given parents the right to request flexible working.
"But Nick Clegg's attempt to pretend this is a family friendly Government too, is a sham," she said.
"David Cameron has already slammed extending paternity leave as 'political correctness.' And they are cutting £1,200 from families with babies.
"How can this Tory-led Government say it's supporting families if they're making mums and kids pay more than the banks?" she added.New paternity leave plans may lead to age discrimination against 20-30 year olds