Goebl is leaving to "pursue other interests" after three years in charge of the show and will be replaced by Primack, who is a former director of the Gagosian Gallery in Los Angeles, former director of auctions at online platform Paddle8, and founder of design consultancy RP Miller.
"We are profoundly grateful to Marianne for her extraordinary contribution to Design Miami," said the event's co-founder Craig Robins. "Her aesthetic and academic sensibilities, balanced and effective management style, and strong relationships were invaluable in cementing Design Miami‘s leadership role within the sector."
Design Miami, which takes place in Miami Beach each December alongside the Art Basel art fair, and in Basel, Switzerland each June, celebrates its tenth anniversary in 2014.
The show was co-founded in 2005 by Robins and Ambra Medda, who left in 2010 and who last year launched online collectible design marketplace L'Arco Baleno.
Goebl, former head of international public relations and partnerships at furniture brand Vitra, took over as director in 2011.
"I have been extremely fulfilled by my time at Design Miami and look forward to an ongoing relationship with the organization, albeit under different circumstances," said Goebl, who will remain a member of the Design Miami board. "I know that Rodman, with his 360-degree experience in the field, will do a wonderful job of shaping the show for its next decade."
Robins added: "We feel confident that Rodman, with his keen understanding of the market, will be a strong director whose innovative ideas will encourage the fair to expand in new and interesting directions while maintaining our excellent relationships with the galleries, designers, sponsoring partners and cultural institutions who have helped make Design Miami great."