Petersfield councillor Julie Butler has been made deputy leader of the council after leader Richard Millard shuffled members.
The change will allow her predecessor, Mr Cowper, to concentrate on his roles as portfolio holder for finance and Whitehill and Bordon.
Mr Millard said: “These are massive tasks because of the council’s determination to be an efficient, low-cost, self-sufficient organisation unreliant on central Government grant. The Whitehill and Bordon project is a huge challenge that has to be delivered properly not just for residents and businesses in the town but for the district as a whole.”
EHDC said Mrs Butler, the portfolio holder for customer services, also has “a wealth of experience” having served the council in key roles since 2007.
Mr Cowper has been leader for more than seven years and deputy leaders for almost two years.
He said that at the age of 68 he wants to spend a “little more time” with his family and on his private interests without diminishing ambitions for the council’s finances and “the amazing town of Whitehill and Bordon”.
This change, he said, gives him the chance to continue to “demonstrate that public sector finances can be completely rethought in a grant-free and tax-free context” while simultaneously “improving services”.
While progress on this has been “exceptionally good”, there is “much more of this job to do”, he said, which will require “focus and commitment”.
Mr Cowper went on to describe his involvement in the Whitehill and Bordon regeneration project as “a huge personal privilege” which has “national and European wide exemplar implications”.
The reshuffle will allow him to employ “the correct level of personal commitment” to see the project “through to the point at which it has acquired its own momentum and is changing the lives of thousands of people for the better”.