The holidays would be on each nation's patron saint day - St David's Day on 1 March, St Patrick's Day on 17 March, St George's Day on 23 April and St Andrew's Day on 30 November.
Mr Corbyn believes the move will "celebrate the national cultures of our proud nations".
Labour says the UK has fewer bank holidays than other G20 countries.
Normally, England and Wales have eight bank holidays a year, Scotland nine, and Northern Ireland 10.
Labour says the average for G20 countries is 12.
Under the policy, the devolved administrations would have the final say on whether to approve the extra bank holidays.
Creating bank holidays is a devolved power in Scotland.
"The four nations that make up our great country have rarely been more divided due to the damaging and divisive policies of this Conservative government," Mr Corbyn will say in a speech on Sunday.
"But where Theresa May divides, Labour will unite our four nations.
"A Labour government will make St George's Day - England's national day and Shakespeare's birthday - a public holiday, along with St David's Day, St Andrew's Day and St Patrick's Day.
"These holidays will be a chance for workers to spend time with their families, in their communities and with their friends.
"But they will also be a chance to celebrate the national cultures of our proud nations."
A Labour government would seek to create four new UK-wide bank holidays, Jeremy Corbyn says.