The Supreme Court rejected two complaints about the conduct of the election from defeated candidate Prime Minister Viktor Yanukovich and said it expected to rule on the fourth and final objection later on Thursday.
Yushchenko, who won last weekend's presidential election by more than 2.2 million votes, said in a late-night television interview that his Our Ukraine bloc's two main allies would each be offered a quarter-share of cabinet posts.
And he revealed that among the top candidates for prime minister was radical opposition figure Yulia Timoshenko, one of the main organisers of his Orange Revolution and a controversial figure in the divided former Soviet nation.
"There is an agreement under which I and my faction will mobilise support for the candidacy of Yulia Vladimirovna [Timoshenko]," the opposition leader said before his interview on the opposition Channel Five network.
In the first concrete indication of the make-up of the new administration, he said the Timoshenko bloc and the Socialist Party of Olexander Moroz would be equally represented in the government.
"The Yulia Timoshenko bloc will get one quarter of ministerial posts, the same for the socialists," Yushchenko said.
Apart from Timoshenko, other candidates under consideration for the premier's post were Moroz, Our Ukraine deputy and owner of Channel Five Petro Poroshenko and Anatoly Kinakh, a leader of a small pro-business party, he said.
Yanukovich, meanwhile, has vowed to exhaust every avenue of appeal, including a full-scale hearing by the Supreme Court, raising the spectre of days' more legal wrangling stretching into January.
Yanukovich is pressing ahead with
his legal challenges
Observers say the appeals are unlikely to scuttle the results of Sunday's election because Yanukovich lacks mass popular support and because the number of irregularities were not enough to narrow the gap between the two candidates.
Yushchenko, who brought his supporters onto the streets for 17 days to protest against fraud that handed victory to Yanukovich in last month's annulled election, is expected to be inaugurated by the middle of January.
Western observers have generally welcomed Sunday's re-run for making great progress towards international electoral standards, unlike the 21 November vote which was annulled by the Supreme Court because of massive ballot-rigging.
One of Yushchenko's first priorities will be to try to heal divisions in Ukraine, with huge tensions between the nationalist Ukrainian-speaking west and the Russian-speaking east and south, a bastion of support for the prime minister.
Relations with Russia, which had backed the pro-Kremlin prime minister in a Cold War-style battle with the West for influence in its former Soviet-bloc backyard, are also seen as a thorny problem.