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The 39-year-old, Ukraine’s record goalscorer who also played for Dynamo Kiev, AC Milan and Chelsea, was officially presented by federation president Andriy Pavelko at a news conference.
Fomenko resigned after Ukraine finished bottom of Group C without a point at the European Championship, having failed to score a goal in their three matches in France.
They lost 2-0 to Germany in their opening game and were beaten by the same scoreline by unfancied Northern Ireland before their campaign ended with a 1-0 defeat to Poland.
Shevchenko, who scored 48 goals in 111 games for Ukraine, joined the national team coaching staff ahead of Euro 2016, replacing assistant coach Olexandr Zavarov.
He retired from playing football after Euro 2012, which Ukraine co-hosted with Poland, having had a successful club career in which he won the Ballon d’Or in 2004 at Milan.