After a week of hard bargaining, he secured agreement on a new coalition government last week that promises to maintain the momentum of Poland's economic reform and its drive to join the European Union and Nato. At the same time, he has made it clear that he wants to open up wide-ranging dialogue with opposition groups and include them in decision-making.
Above all he has pledged a thorough and impartial investigation into the allegations against Mr Oleksy, which are being examined by the country's senior military prosecutors.
"I will do everything to ensure that the government will be fully credible in the legality of its actions and respect for law," Mr Cimoszewicz told the United States Assistant Secretary of State, Richard Holbrooke, who visited Warsaw last week. He conceded, however, that if the allegations against Mr Oleksy were found to be true, there would be "repercussions on the entire political situation".
Many Poles fear that the scandal surrounding Mr Oleksy has already had serious repercussions, harming their country's international standing and raising question marks against its suitability for Nato and EU membership.
Mr Holbrooke himself conceded that Poland's handling of the crisis was being "keenly watched" by Washington, adding that, "they [the Poles] recognise themselves that there are some democratic procedures that must be worked through in the next few months".
Most Western diplomats in Warsaw admit to being disconcerted by the KGB allegations - which have been denied by Mr Oleksy himself - but are withholding judgement pending the results of the investigation.
"These are very serious charges and the longer this goes on, the worse it looks," said a diplomat. "The sooner things are brought out into the open and clarified, the better."
The storm over Mr Oleksy, a former Communist, broke in the last week of Lech Walesa's presidency in December. Mr Walesa claimed to have material showing that Mr Oleksy spied for the KGB from the early 1980s up until he became Prime Minister last March.
Mr Oleksy described the allegations as a "dirty provocation", motivated by Mr Walesa's desire for revenge following his defeat at the hands of another former Communist, Aleksander Kwasniewski, in November's presidential election. Mr Oleksy admitted, however, to a long friendship with a Russian diplomat who later turned out to be a KGB officer. He also admitted that, under the circumstances, the friendship had been "imprudent".
Since the overthrow of Communism in 1989, Poland has experienced six changes of government and seven changes of prime minister. However, for all the dramas in the Sejm (lower house of parliament) the country's economy has boomed regardless, recording impressive growth rates for four years in succession and an ever-increasing shift towards the private sector.
The departure of Mr Oleksy has rung more alarm bells than those of his predecessors because it raises awkward questions about his formerly Communist party, the Democratic Left Alliance (SLD), the dominant force in Polish politics today.
For Mr Walesa and the heirs of Solidarity, it confirms what they have said all along: that for all the SLD's claims to be a party of reform- minded Western-style social democrats, there is something rotten at its core. Even those more favourably disposed towards the party concede that they do now wonder what other skeletons may be rattling in its cupboard.
Both friend and foe acknowledge, however, that in choosing Mr Cimoszewicz as Mr Oleksy's successor, President Kwasniewski has made a shrewd move. Although he was a member of the old Communist Party, Mr Cimoszewicz, 45, never held a high position within it, in marked contrast to both Mr Oleksy and Mr Kwasniewski. Since 1989 Mr Cimoszewicz has stood out as being an independent spirit, frequently refusing to toe the SLD party line.
As justice minister in 1993, he became famous for his "clean hands" campaign aimed at ensuring probity in public life, including among former Communists. Last year, he caused further consternation in the SLD camp by initially refusing to support Mr Kwasniewski in his election campaign.
The SLD is clearly hoping that the new Prime Minister will help to restore some of its lost credibility. It may also back President Kwasniewski's recent proposal to open up the country's secret service files to determine exactly who did inform for the old regime.
But the SLD is not feeling too contrite. Last month it selected Mr Oleksy to succeed Mr Kwasniewski as party leader.