Hoy-Taylor was head of design at the internet gift and gadget retailer. Prior to joining Firebox he handled web design for a number of leading record labels.
At Tangent, Hoy-Taylor will be involved in all aspects of web and e-mail design for clients, which include the Labour Party, Borders Books, the National Lottery, Nike, Coca-Cola, EMI, Universal Music, Capcom, Kwik Save, Mercedes Benz and HarperCollins Publishers.
Greg Jackson, Tangent's director of online strategy, said: "In appointing John we demonstrate our commitment to appoint only the very best.
"John is an exceptionally knowledgeable creative who has an outstanding track record in e-mail commerce, website and e-mail design, which he can bring to bear across all our clients.
"He will ensure that we continue to maximise return from the digital campaigns we deliver and add value to our client's businesses."
Hoy-Taylor said: "I joined Tangent because of their impressive reputation in the digital and DM industry, the fact they are growing fast and have a very impressive client list.
"I'm looking forward to the challenge of delivering highly creative digital work that generates strong results for their wide portfolio of blue-chip clients."