The question does not specify which particular Ukrainian elections we are talking about. There have been seven presidential elections since Ukraine became independent from the USSR in 1991, see Ukrainain presidential elections:
Since the establishment of the position of the President of Ukraine in 1991, the presidential elections have taken place seven times: in 1991, 1994, 1999, 2004, 2010, 2014 and 2019.
Whether elections are considered free and fair depends on whose opinion one asks. I will therefore quote here an answer to another question, specifically addressing this point:
While democratic elections can differ in many details, there is a widely accepted set of standards applied e.g. by the OSCE election monitors. They are routinely reporting on elections in various countries, and usually produce a set of suggestions for improvements. If you look at the assessment e.g. for Russia, Canada, and Iceland, you will find a vast difference in tone and conclusions, from 'we don't detailed monitoring, but you shoud look into campaign finance transparency and a few other things' to 'we need 500 watchers.'
Among the seven electuions the following ones were called in Question:
2004 Ukrainian presidential election
The election was fought mainly between Viktor Yushchenko and Viktor Yanukovych, perceived respectively as a pro-western and a pro-Russian candidates. Yanukovych was first declared a winner, but the elections were widely considered as rigged, and the results had to be revised
The subsequent events led to a political crisis in Ukraine, with widespread peaceful protesters, dubbed the "Orange Revolution", calling for a re-run second round election. The Ukrainian Supreme Court annulled the official run-off results and ordered a repeat of second round ballot.2
The final re-run ballot was held on 26 December. Viktor Yushchenko was declared the winner with 52 percent of the vote to Yanukovych's 44 percent. Western observers reported that the re-run ballot was considered overall fairer than the previous ballots.2
2010 Ukrainian presidential election
This time the election was won by Viktor Yanokovych. Although the question of fraud naturally came up in view of the previous election, the election was largely accepted as fair.
According to all international organizations observing the election, allegations of electoral fraud in relation to the first round ballot were unfounded, they declared that the conduct of the elections was within internationally recognized democratic standards and a testament to the will of the people of Ukraine.[171][172][173]
A December 2009 poll found that 82 percent of Ukrainians expected vote rigging, those fears were shared by some election observers, both international and domestic. The latter also fearing the lack of an independent exit poll; which they see as essential to deterring vote fraud.[174]
Yulia Tymoshenko, Ukraine's Prime-minister and one of the main candidates who sought election in the poll stated that: "We will not challenge any election returns to avoid tremors, which may bring about instability in this country. If the people elect their president, and this is not Yulia Tymoshenko, I will take this choice easy, for sure"[175]
Former President Leonid Kuchma also excluded the possibility of a third round ballot. According to Kuchma, "during the election campaign in 2004 the decision about holding the third round was political and it will not be repeated.
2014 Ukrainian presidential election
Viktor Yanukovych was ousted in the course of the 2014 Revolution of Dignity, and new presidnetial elections were called. Petro Poroshenko won the election, which was largely recognized as valid, even by Russia:
Despite Russia's earlier protest at rescheduling the election and the general tense relation between the countries at the time because of the annexation of Crimea and the Russian military intervention in Ukraine, Russian President Vladimir Putin recognised the vote.[106]
The leaders of the self-proclaimed Donetsk People's Republic and Luhansk People's Republic, controlling large parts of the Donbas region of Eastern Ukraine, declared that the regions had made their choice shown in the results of the status referendum of 11 May.[14]
US President Barack Obama congratulated Petro Poroshenko with his victory by telephone 2 days after the election.[107] This was also done by President of the European Commission José Manuel Barroso and European Parliament President Martin Schulz and other EU leaders such as German Chancellor Angela Merkel and French President François Hollande.[108][109]
See also
2019 Ukrainian presidential election
Thsi election was mainly fought between Volodymir Zelensky and Petro Poroshenko. The results of the elections were never in doubt - Poroshenko recognized his defeat:
Exit polls during the second round of voting predicted that Zelenskyy would win with more than 70% of the votes.3 With only 3% of the votes counted, the CEC confirmed similar preliminary results.[128] Poroshenko conceded the results of the election in a speech soon after the polls closed and exit-poll data was released.[128][129] He wrote on Twitter: "We succeeded to ensure free, fair, democratic and competitive elections... I will accept the will of Ukrainian people."[130]
Results of the second round by total voters number
Finally, note that in 2014 and 2019 the participation of the Ukrainians living in the regions of Donetsk, Luhansk and Crimea was limited, due to political reasons and the difficulty of organizing polling in these regions.
