Zvarych moved to Ukraine in 1991 with the intention of pursuing an academic career, but soon after became involved in politics. In 1992, he and Slava Stetsko founded the Congress of Ukrainian Nationalists, a right-wing party. He renounced his U.S. citizenship in 1995. Along with fellow politician Ivan Lozowy this made him one of the first former Americans to renounce U.S. citizenship in favour of Ukrainian citizenship. A notification confirming his loss of citizenship appeared in the Federal Register in June 1997 with his name listed as "Roman Mychajlo Zwarycz". Zwarych ran for a seat in the 1994 election for a single-mandate seat representing a district of Kyiv in the Verkhovna Rada, and received 70% of the vote but was not elected due to his failure to meet the voter turnout threshold of 50% mandated by the electoral law at the time. He was eventually elected in the 1998 election from a party-list proportional district. Thereafter he sat in the Verkhovna Rada for six years, serving on various committees including the Committee on Legal Reform and the Committee on European Integration. Outside of the Verkhovna Rada he also moonlighted as a lawyer; Ukrainian courts had no requirement for practitioners of law to hold certifications or pass a bar examination. On one occasion Zvarych successfully defended a family against eviction. More importantly, during the Orange Revolution in the midst of the 2004 presidential election, he successfully argued a case on behalf of Viktor Yushchenko to prevent the creation of Ukrainian voting districts for Ukrainians in Russia. In February 2005, with Yushchenko having emerged victorious in the election, he appointed Zvarych to head the Ministry of Justice. In April 2005, articles in Ukrayinska Pravda and other media outlets accused Zvarych of lying about holding a Ph.D. from Columbia University. A spokesperson for the university had confirmed to a Ukrayinska Pravda reporter that no person by his name had earned a degree there. Zvarych called a press conference the following month in which he admitted the truth of the accusations about the Ph.D.; in his clarifying remarks, he claimed to have been an "all but dissertation" student and to have worked as an adjunct lecturer at Columbia University, being informally referred to by colleagues and students as "professor" without having held that academic rank. He accused the Ukrainian diaspora and the Komsomol of Ukraine of orchestrating a political smear campaign to blow the misunderstanding out of proportion. In the 2014 Ukrainian parliamentary election Zvarych was a candidate of Petro Poroshenko Bloc; placed 82nd on the electoral list. But the party only won 63 seats on the electoral list; hence he was not elected into parliament. But he returned to parliament nevertheless on 15 March 2018 to take the place of Valery Pakzkan who was just elected head of the Accounting Chamber of Ukraine.
