The grant will be available to single parents and households where both parents are in work. Balls said he plans to raise the banking levy by £800 million a year to fund the move.
Children aged three and four currently receive 15 hours of free care a week, but Labour want to increase this to 25 hours a week.
The shadow chancellor will outline his plans later in his keynote speech at the Labour Party conference in Brighton.
He is expected to say: "Childcare is a vital part of our economic infrastructure that, alongside family support and flexible working, should give parents the choice to stay at home with their children when they are very small and to balance work and family as they grow older.
"But for many families, high childcare costs mean that it doesn't even add up to go to work. So to make work pay for families, we must act."