Elwood will head Fallon's design operation, Fallon Design, formerly Duffy Design, and will report directly to the agency's creative director and managing partner, Richard Flintham.
The appointment comes as Fallon looks to move its design element closer to the core of its creative output.
Duffy Design, which was previously headed by Adam Whitaker, parted company with Fallon earlier this year. Fallon Design has now relocated to Fallon's offices.
Elwood said: "It has been a pleasure working at AMV. However, the opportunity to work with Richard and Andy McLeod was too tempting.
"Fallon has always had the kind of creative output and culture that I admire and I cannot wait to become part of that."
Elwood spent the past three years with AMV, where he worked on accounts including Guinness, The Economist and the NHS.
He began his career in advertising as a typographer at Leo Burnett. From there, he moved to J. Walter Thompson, before relocating to Euro RSCG to head the agency's typography department.
Flintham said: "We are trying to do more work across more media. Mark is there to ensure we keep the creative bar as high as humanly possible as we develop."