Graduated with a bachelor's degree in agronomics from the National Agrarian University. Oxford College graduate. In 1995 founded a small grain trading enterprise focusing on grain exports out of Ukraine, which through the years grew into a present Kernel. Chairman of the board and majority shareholder of Kernel Holding S.A. since 2007.
2002-2006, Verkhovna Rada parliamentary deputy of the 4th convocation. Fellow of the Verkhovna Rada Finance and Banking Committee. Until December 2004, member of the United Ukraine faction, European Choice group and Regions of Ukraine faction. From June 2005, member of Yulia Tymoshenko Bloc's faction.
In June 2010, Verevskiy crossed to the Stability and Reform coalition formed by the Party of Regions, Lytvyn Bloc and Communist Party factions. Since October 2010, member of the Party of Regions faction.
In 2012, US Forbes Magazine valued net worth of Andrey Verevskiy at USD 1 billion. In April 2016 the Ukrainian magazine Focus estimated his wealth at $642 million.
Verevskiy was placed at number 46 on the electoral list of Party of Regions during the 2012 Ukrainian parliamentary election. He was re-elected into parliament. The Higher Administrative Court of Ukraine stripped Verevsky of his seat in parliament on 5 March 2013 because he simultaneously was parliamentary deputy and headed a commercial entity.