Atkinson was employed by British Swimming as the national performance director for disability swimming and led the nation's athletes to 39 medals at the London 2012 Paralympics.
He had been among the names mentioned to replace Michael Scott as the performance director of the non-disabled team following the Australian's departure back in November.
Scott left upon findings of review into the performance of Britain's swimmers at the London 2012 Olympics, which saw them fail to hit their medal target of five to seven, winning just three.
The review suggested that Scott be permanently based in the UK as opposed to splitting his time spent in the nation with that of his native Australia however he couldn't commit to it.
But Atkinson won't be replacing him as he takes up the role of national high performance director for Swimming Canada in Ottawa, a job he insists he couldn't pass up.
"I've had a successful 12 years across different roles within British Swimming and I will take with me fond memories," said Atkinson, who will lead his post at the end of February.
"However, the opportunity to lead the Olympic programme in Canada was too good a challenge to turn down.
"I'd like to thank everyone involved in the swimming and disability swimming programmes for their support over that period.
"I've made a lot of friends within British Swimming and I wish everyone the best for the future."
Former national performance director Tim Reddish will lead disability swimming programme on an interim basis to ensure continuity and development of plans for Rio 2016.
Meanwhile British Swimming is due to announce the appointments of the non-disabled performance director and head coach next week.