The Premier League team said on their Web site (www.liverpoolfc.tv) an agreement had been reached with the 27-year-old Bayer Leverkusen player.
Voronin, a free agent at the end of the season, has also had spells in Germany with Cologne, Mainz and Borussia Moenchengladbach.
He was a member of Ukraine's squad at the World Cup finals in Germany last year.
