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.
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".
Rahm Emanuel is an Illinois congressman if he accepts the position of chief-of-staff, he would be responsible for much of the internal management of the new administration.
With the country in the throes of an economic slowdown and part of the global financial crisis, the post of treasury secretary will be another key post, our correspondent adds. Likely contenders for the post reportedly include former Treasury Secretary Larry Summers and Timothy Geithner, the current head of the New York Federal Reserve.
With the business of preparing for government under way, Mr Obama will from Thursday start receiving the president's daily CIA briefings, which will include updates on covert operations.
Projected results from Tuesday's election have yet to be announced for the states of North Carolina and Missouri, which are believed to be too close to call. But with most precincts tallied, Mr Obama's share of the popular vote stands at 52.3%, compared with Mr McCain's 46.4%.
Turnout was reported to be extremely high - in some places "unprecedented" in what many Americans said they felt was a historic election.
It was predicted that 130 million Americans had voted - the highest turn-out since 1960.
The entire US House of Representatives and a third of US Senate seats were also contested in Tuesday's elections.
The Democrats increased their Senate majority by five seats, but fell short of the 60 needed to stop blocking tactics by Republicans.
They also increased their majority in the House of Representatives, gaining 20 seats to give a total 252, leaving the Republicans with 173.
Copyright Speakers Corner 2017