Up replaces Good Relations in the contract, which is initially for 12 months.
Internet Matters is supported by UK ISPs including BT, Sky, TalkTalk and Virgin Media. All agencies were required to pitch to PR representatives of the ISPs as well as Internet Matters.
The agency is briefed with establishing the organisation as a leading authority in child online safety and parental education fields.
Up Communications has launched its first major campaign for the brief. Called 'Protect Their Curiosity', this raises the topic of online safety and was picked up by various national media outlets including Channel 4 News, Sky News, Good Morning Britain and Radio 4 Women's Hour.
Carolyn Bunting, MD of Internet Matters, said: "At Internet Matters we have a simple ethos that involves encouraging parents to learn about online issues, talk to their kids and deal with the situation directly. We’re looking forward to working with Up to help share that message."