The agency picked up the brief after a pitch against Bartle Bogle Hegarty and Farm.
The DCSF kicked off its review of the internet safety project in October last year.
The pitch followed an independent review undertaken by the child psychologist Dr Tanya Byron that looked at the risks that children face from exposure to inappropriate material on the internet.
The review recommended that a public information campaign be launched to help educate children and their parents about the dangers surrounding potentially harmful content, and give advice on what can be done to ensure that young people can safely make the most of what the internet has to offer.
The campaign will be launched during Safer Internet Week, which begins on 8 February, and will establish a new "green cross code for the online world", a concept that was introduced by Ed Balls, the Secretary of State for Children, Schools and Families, last month.