The parliament also voted to dismiss the Central Election Commission as part of the compromise. The opposition had accused that electoral body of incompetence in tallying and certifying the results of the 21 November vote.
Parliamentary speaker Volodymyr Lytvyn said credit should be given to outgoing President Leonid Kuchma, who signed the measures while lawmakers stood and cheered.
"I believe we can thank the president of Ukraine, because today we made a mutually appropriate decision," Lytvyn said.
Supporters of opposition candidate Viktor Yushchenko had pushed for electoral changes to close loopholes for fraud in the Supreme Court-ordered repeat of the late-November presidential runoff election, expected to take place on 26 December.
But they had resisted the constitutional changes -- called for by his opponent, Prime Minister Viktor Yanukovych -- that would transfer some presidential powers to parliament.
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