The return of the divisive and headstrong Saakashvili, who became governor of Ukraine's Odessa region after being Georgian president from 2004 to 2013, poses a strong challenge to Ukrainian President Petro Poroshenko, who once was Saakashvili's patron.
Earlier, Polish border guards let Saakashvili out of the country but warned him about possible problems with the Ukrainian authorities.
Saakashvili has accused the Ukrainian authorities of using pressure tactics to deter him from returning to Kiev, where he has launched a campaign to unseat Poroshenko. But Saakashvili quit as governor of Odessa in November, accusing Poroshenko of abetting corruption.
Saakashvili took power in Georgia after a peaceful pro-Western uprising, known as the Rose Revolution, in 2003.
Ukraine's Interior Ministry said that 11 policemen and five border guards were injured in yesterday's affray. According to Groysman, Saakashvili committed an "attack on Ukrainian statehood".
On July 26, Poroshenko revoked Saakashvili's Ukrainian citizenship when it was discovered that he had violated the law by providing incorrect information on his citizenship application.
"I crossed the Polish border with a valid Ukrainian passport, the Poles stamped it", Saakashvili told reporters according to Ukrainian outlet Unian.
The breakthrough across Ukraine's border occurred when Saakashvili and people traveling with him, including his wife, son, and several Ukrainian MPs, were stranded in the neutral zone between Ukraine and Poland. "This is a matter of national security", Poroshenko said. But the train was held at the station for hours - and then announced that it would not leave with a person who had no permission to enter Ukraine.
He said Saakashvili should have contested the decree stripping him of citizenship in court if he disagreed with it.
Saakashvili denies the allegations and says Georgia's extradition request was made on behalf of "oligarchs" who fear his presence in Ukraine.
After crossing the border Saakashvili thanked his supporters, saying all of them were heroes.
At the Medyka border, supporters expressed hope that Saakashvili could deliver some of the same types of reforms in Ukraine.
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