Prior to Saatchis, Atkinson was chief executive at DM agency Interfocus and before that managing director at Tequila, where he was responsible for launching the agency's network of Asian offices.
Horne, who is understood to have left because of family reasons, departed in October to set up his own consultancy in the West Country.
Terry Hunt, EHS Brann chairman, said: "Atkinson will spearhead the next phase of growth, ensuring clients get the very best in direct marketing, digital and data skills."
Atkinson will report to Hunt and CEO Andrew Harris.
The appointment of Atkinson follows the recent promotion of Trevor Chambers and Lu Dixon to the board as executive creative directors.
The agency is now looking to put in place a senior creative management team.
Havas-owned UK agency Brann merged with London-based EHSrealtime in January 2002.
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