The agency scooped the account following a three-way pitch, which was handled by the in-house marketing team at United Biscuits.
Inbox will take responsibility for developing digital strategies across the company's portfolio of brands, which also includes Jacob's Biscuits, KP Nuts, McVitie's, Skips, Penguin and Go Ahead!
Initially, the agency will create an e-CRM campaign for the Go Ahead! range of snacks, but future campaigns will cover a range of digital marketing activity, including online advertising, mobile marketing, web development and online media strategies.
This is the first time the company has consolidated its digital advertising business into one agency.
In 2002, United Biscuits appointed Wheel Group's Abel & Baker, Oyster Partners and Cordiant's XM London to its digital roster, and worked with them on an individual project basis.
Oliver West, the marketing controller for McVitie's, said: "Inbox Digital impressed us with a sound, highly strategic business case and some first-class creative ideas. We're excited to be working with the agency to develop strong consumer communications for our well-loved brands via new technology channels."