The campaign, by Ogilvy, which launches this week, marks the biggest investment in the brand by Unilever for several years.
The ad shows a mother consulting a recipe book for ideas of what to cook with leftovers from Christmas dinner.
Print and TV executions will suggest several recipes, such as a "chill out turkey salad" and a "bubbly jubbly squeak" take on bubble and squeak.
The ads also introduce the strapline, "Bring out the best in Boxing Day". In addition, the executions direct consumers to hellmanns.co.uk, where the recipes are available.
The "12 Days of Christmas" TV ad, by Lowe, which ran from 1992 to 2004, featured a choir singing a version of the carol, with the lyrics changed to describe Christmas dinner leftovers.