He will take up the job, which was advertised at £125,000 a year, in November.
Hughes succeeds Neil Hunt, who left the society in January without serving his notice period after seven years in charge.
Ruth Sutherland, who has been acting chief executive since Hunt's departure, will return to her role as chief operating officer.
In a statement, Alastair Balls, chair of the society said: "This is a critical time for the society as we implement government-sponsored dementia strategies.
"Jeremy will provide the insight, leadership, campaigning skills, commitment and energy to drive this forward successfully."
Balls said Breakthrough had become "a powerful influence on the NHS" and that Hughes's experience in this area was "particularly attractive to the board of the society as it continues to grow in both size and influence".
The society recently restructured in a bid to win more government contracts, a move that has angered some long-standing volunteers.
Hughes has been chief executive at Breakthrough since January 2005. Its income grew rapidly from £14.5m to £24.4m in his first year in charge but has since fallen to £16.3m.
Before joining Breakthrough, Hughes was head of external affairs at the International Federation of Red Cross and Red Crescent Societies. He has also been director of marketing and income generation at the British Red Cross and director of public affairs at Leonard Cheshire Disability.
In a statement, he said: "I look forward to working closely with all involved with the society to meet the challenges of the new decade. Everyone must play their part to ensure that people living with dementia have better prospects in 2020 than they do today."
He said he would be sad to leave Breakthrough, where "our vision of a future free from the fear of breast cancer could have been seen as a long term aspiration. Today that is no longer the case - it is now very achievable".