The two candidates gained the most votes in yesterday's election, which saw current President Viktor Yushchenko lose out.
Other candidates included former Central Bank chairman Sergey Tigipko and former foreign minister Arseniy Yatsenyuk.
Mr Yanukovich has an 11% lead over Ms Tymoshenko following the first round of votes.
However, political analysts expect Ms Tymoshenko to pick up a higher proportion of second round votes from the defeated candidates.
Ms Tymoshenko helped lead the pro-Western Orange Revolution against Mr Yanukovich's tainted 2004 presidential election victory.
Mr Yanukovich was subsequently replaced by Mr Yushchenko when the 2004 result was annulled.
