Barack Obama has started forming his administration by asking Rahm Emanuel, a former adviser to President Clinton, to be his chief-of-staff.
US President-elect Obama is expected to appoint a new treasury secretary soon.
He has until his inauguration on 20 January to select his senior officials. President Bush has pledged his complete co-operation during the transition.
Mr Obama was elected the first black US president on Tuesday with a resounding win over Republican rival John McCain.
There has been speculation Mr Obama will ask Defence Secretary Robert Gates to remain in his post.
Mr Gates is broadly respected by both parties and would reflect a more bipartisan administration, says the BBC's Jane O'Brien in Washington.
Mr Obama's victory was widely welcomed around the world.
UK Prime Minister Gordon Brown called Tuesday's poll historic and said he and Mr Obama "share many values".
Chinese President Hu Jintao said he looked forward to strengthening dialogue. France's Nicolas Sarkozy said the poll had raised "enormous hope".