The merged companies, both part of Havas Advertising, will be known as Arnold Interactive UK, and will operate as a subsidiary of Arnold Worldwide Partners.
The Zinc brand will be scrapped and some redundancies are expected. Georgia Hall, Zinc's joint managing director, and creative director Ray Howard have both resigned.
Hall's fellow joint-managing director, Ken Frakes, becomes managing director and executive creative director of the new entity, while Bruce Winfield, managing director of AMX, has been named chief executive. All staff will be moved to AMX's offices within a month.
Frakes claimed the merged company would have about 60 staff. He said: "Redundancies will be minimal and mostly within administration. AMX currently has about 47 staff."
"AMX is known for its creative strengths, and we are known for our work in the marketing arena, so together we can build a technically stronger creative team," added Frakes.
He said that Zinc's clients, which include Expedia, Warner Village and Computer Weekly, will all be retained. AMX clients include Barclays, Channel 4 and Toyota.