Eriksson was appointed on a five-year deal in October to replace Dutchman Charles van Commenee but asked to be released from his contract in order to return to Canada to be with his family.
"Words cannot describe how disappointed I am to take this step," said Eriksson, who was in charge of the British Paralympic team at the 2012 London Games.
"There is no bigger job in athletics anywhere in the world. At present I have no plans but accept that if I am to take any other job in sport it will be a step down.
"Athletics in Great Britain receives the best possible support through the National Lottery and that, coupled with the performance structure here, means it is every coach's dream to hold this position.
"However no job is more important than family and children, and personal circumstances mean that mine need me to be back in Canada," added the 60-year-old, who was born in Sweden but moved to Canada in 1987.
Eriksson will continue as head coach until the end of June, overseeing the European Team Championships in Gateshead, northern England.
Performance Director Neil Black will take on the head coach duties for the remainder of the outdoor season, including leading the team at the world championships in Moscow in August.
- Sports & Recreation