The DfE has appointed PR agency Access Point to deliver the campaign, which will run from the beginning of December to the end of January.
Every Argos receipt issued at its 364 stores across England will alert parents of two-year-olds to the 15 hours of free childcare for which they may be eligible.
The first phase of the campaign was carried out in September through a mix of poster and radio adverts that ran across 26 local authorities.
A spokesperson for the DfE said: "We know that good quality early education can make a huge difference in levelling the playing field and improving a child’s life chances, and this free childcare entitlement gives children crucial support that could make all the difference to how well they do at school and beyond.
"Parents who think their toddler may be eligible should check to make sure they don’t miss out."
The campaign is being backed by childcare minister Sam Gyimah who wants to promote the benefits of good quality early education among parents and the financial help available to them.
By Anna Reynolds, PR Week