Between barricades of tires and impromptu memorials to the victims of Ukraine’s revolution, Mikheil Saakashvili stops to pose for pictures and shake hands. “You showed us how to fight Russia,” says a gray-haired man in a camouflage jacket, embracing him on Institutska Street, a front line in last week’s climactic clashes in the capital.

As the former president of the ex-Soviet nation of Georgia, Mr. Saakashvili certainly knows all about confronting Russia and Vladimir Putin. He also lost a chunk of his country in the process. Now he is here in Ukraine, a country he knows well from his youth, to advise its new leaders on how they can revive the economy as well as keep their nation intact from Russian’s potentially crippling intervention.

Mr. Saakashvili studied law and served in the Soviet military in Kiev, altogether for seven years. He has many friends and knows the major politicians, who seek out his advice.

His own rise to power also began with the victory of a youthful street uprising over a corrupt and autocratic post-Soviet leader—Georgia’s Rose Revolution of 2003. Thirty-seven years old at the time, Mr. Saakashvili became the youngest president in Europe. As president, he overhauled Georgia’s government and economy, pushing the country hard westward, along the way making many foes, most perilously Mr. Putin.