At Fallon, Djaba, 29, will take charge of the agency's Velvet, Timberland and BBC accounts, while retaining some responsibility for new business.
Djaba joined O&M in 1997. He left the main agency briefly in 2001 to become part of the management team of O&M's spin-off agency, English.
However, English folded after just seven months and Djaba, who had been in charge of its account planning and handling, returned to O&M and took the position of new-business director.
"Each account at Fallon has great work; there are no skeletons," Djaba said.
"When you watch the reel, each piece of work resonates - it's not just funny, but true to the brand and how consumers understand it," he added.
Djaba started his career at IMP, working on Masterfoods and National Australia Group Banks. He later joined O&M to work on Lever Faberge's Impulse, among other brands.
Laurence Green, Fallon's planning partner, added: "Magnus is a new-school account director - smart, collaborative and passionate about creative work."