He is the 2012 Olympic Champion, the 2010 and 2011 World Champion, and the 2007 and 2009 World silver medalist. He is also the 2005, 2007, 2008, 2009, 2011 and 2012 European Champion on that event. He won the Universiade 2009 in Belgrade. In 2010 and 2011 he was elected Hungarian Sportsman of the year for his achievements.
At the 2012 Summer Olympics Berki competed in and won the pommel horse competition, winning the gold medal with a score of 16.066, exactly the same score as British athlete Louis Smith, but was awarded the gold on a higher execution score. Smith's GB team mate, Max Whitlock won the bronze medal.