The former Dynamo Kiev midfielder and Metalist Kharkiv coach was unveiled on Wednesday as the successor to Oleg Blokhin, who resigned in September following an unsuccessful Euro 2012 campaign in a tournament the country co-hosted with Poland.
The Football Federation of Ukraine reported on their website that Fomenko was the unanimous choice of its executive committee. Former England boss Sven-Goran Eriksson and current QPR manager Harry Redknapp had previously been linked with the role.
Fomenko told the Ukraine FA website: "I want to thank the board and president of the FFU for their trust. I understand the responsibility entrusted in me and challenges that face the national team of Ukraine.
"Our primary objective is to get to the finals of the World Cup in Brazil, and for this we need to take at least second place in our qualifying group."
Fomenko, now 64, made 212 appearances in eight years with Dynamo during the 1970s and also won 24 international caps.
As a coach, he helped establish Metalist as a force in the domestic Premier League and also has previous international experience with Guinea. His most recent job was with Russian second-tier side Salyut Belgorod.