Udovenko entered diplomatic service in 1959 as 1st secretary, counsellor at the Department of International Economic organizations of the Ministry of Foreign Affairs of the Ukrainian Soviet Socialist Republic.

From 1977 to 1980, he was director of the Interpretation and Meetings Division at the Department of Conference Services of the United Nations office in New York City.

In 1980–1985, he was Deputy Minister of Foreign Affairs of the Ukrainian Soviet Socialist Republic, and was assigned the rank of ambassador extraordinary and plenipotentiary in January 1985.

During the 3rd and 4th convocations of the Verkhovna Rada, he was chairman of the Parliamentary Committee on Human Rights, National Minorities and Inter-ethnic Relations.

In the 2006 parliamentary elections, he was again part of the Our Ukraine list, but declined laying down his parliamentary mandate[7][8] during the political crisis in the spring of 2007, when more than 150 MPs from Our Ukraine and Yulia Tymoshenko Bloc resigned from the parliament, giving the president the legal grounds for dissolving the Verkhovna Rada.

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