The Labour leader will also pledge to increase statutory paternity pay (£138.18 per week) by more than £120 a week to £260 a week.
Legislation around shared parental leave comes into force in April, but government predictions show only 5,700 men are expected to apply for shared parental leave over the next 12 months.
Currently just over half (55%) of new fathers take the two weeks' paid leave, which was implemented in 2003. Research has found many working fathers do not take the full two weeks off due to financial pressures.
The plans will be funded by savings made from tax credits, Labour claims.
Employment partner at law firm Weightmans Phil Allen said the proposal could "enable a more level-playing field for those employers who do currently allow longer paternity leave and who pay greater paternity pay, when compared with those who currently do not".
He added: "It will encourage all employers to treat fathers of new borns in an appropriate way – four weeks leave is not a significant problem for most employers.
“The rate of statutory paternity pay will assist those in lower paid jobs, but will still be a blocker for more highly paid employees unless their employers enhance paternity pay. These will sit alongside the new right to shared parental leave and pay and together may significantly increase the likelihood of fathers taking more time off to care for their children.”
Working Families CEO Sarah Jackson welcomed the proposals. She said: "Increasing paternity leave from two weeks to four weeks, and doubling the rate of statutory paternity pay, will be welcomed by many families and should be by business leaders too. It’s an opportunity to re-engage with a core group of employees, to help them to give their best at work by recognising that they also want to give their best at home."
Dads not eligible
Separate research from the TUC has found only 40% of working dads will be eligible to take shared parental leave, because their partner is not in paid work.
Shared parental leave legislation does not allow mothers who are self-employed or not employed to share maternity leave or pay.
TUC general secretary Frances O’Grady said: “The UK is still decades behind other European countries when it comes to rights and financial support for new fathers.
“If politicians are serious about men playing a more active role after their child is born they must increase statutory paternity pay, and look at introducing some father-only leave that isn’t dependant on their partner being in work.
“Employers must also work more closely with unions, who often secure better paternity rights for dads.”