Assuming she is confirmed by the Senate, Ms Albright, the daughter of a Czech immigrant who fled the Communist takeover in 1948, would become the first woman in US history to hold the most prestigious cabinet job, which is also the fifth-ranking post under the country's constitution.
In other moves, announced by Mr Clinton in an Oval Office ceremony yesterday, Anthony Lake, currently national security adviser, will take over from John Deutch as director of the troubled Central Intelligence Agency, while Mr Lake will be replaced by his deputy, Sandy Berger. Strobe Talbott is expected to remain as Deputy Secretary of State.
Originally, the White House had signalled that Mr Clinton would move to make good the massive post-election exodus from his cabinet within days of his victory on 5 November. But as with the selection of his first cabinet four years ago, the process has become far more protracted than intended.
But, in the past few days, the 59-year-old Ms Albright, a strong advocate of intervention in Bosnia and the expansion of Nato, and the spearhead of Washington's effort to oust Boutros Boutros Ghali as UN Secretary General, had clearly emerged as favourite, as the star waned of former front runner, the ex-Senate majority leader George Mitchell.
Seen primarily as a loyal and forceful executor of policy, rather than a grand strategist, she is unlikely to usher in any great changes in US foreign policy, at least not in the early stages. But she is likely to be a far more assertive promoter of policy than her predecessor, the cautious Warren Christopher - no mean attribute when the State Department budget and foreign aid are under unprecedented pressure from a Republican- controlled Congress profoundly suspicious of all things foreign.
Even so, Ms Albright's approval by the Foreign Relations Committee, chaired by the arch-conservative Jesse Helms, is hardly in doubt, thanks to her staunchly anti-communist personal background and her forthright championing of US interests - not least in her excoriation of Fidel Castro, a particular bete noire of Mr Helms.
Apart from Mr Mitchell, the other finalists in the state department search were the departing Georgia senator Sam Nunn, and Richard Holbrooke, the architect of the Dayton peace accords for Bosnia. Mr Holbrooke could succeed Ms Albright at the UN in New York.
For his part, Mr Cohen, a moderate three-term senator from Maine deeply versed in defence policy, was always a prime candidate to succeed William Perry at the Pentagon, once Mr Clinton had signalled his wish for accommodation with Capitol Hill by appointing at least one prominent Republican to a top administration post. Not since Richard Nixon made John Connally Secretary of the Treasury in 1971 has a senior cabinet member served under a president of a different party.
Like Ms Albright, 56-year-old Mr Cohen is not squeamish about the use of US military force. An early advocate of going to war against Saddam Hussein over Kuwait, he insists the US must maintain a forward defence strategy, underpinned by more mobile forces.
The two appointments could see both ends of Pennsylvania Avenue more united on foreign policy than at any point in Mr Clinton's tenure. If so, it will be a good omen for the other cabinet posts the President must fill, including transportation, housing and energy.