Robinson joins the agency next month and will be responsible for overseeing digital work across all of JWT's clients, including HSBC, Kraft Foods and Nokia.
He will report to Russell Ramsey, the agency's executive creative director, and will work closely alongside the digital creative director Paul Banham, who joined JWT from Archibald Ingall Stretton in August last year.
Robinson has been at Dare for just over a year, working on campaigns for brands such as BMW, Premier Inn and Vodafone.
Last year, he also helped create the "spark something" campaign for Sony Ericsson, which saw thousands of space hoppers invade the Yahoo! homepage.
Ramsey said: "Olly has worked on some really exciting digital projects. His work is exceptional and his talent is perfect for JWT."