Sviatchenko was, during his youth playing years, captain of the FC Midtjylland squad. During his first year as a U/19 player, he and his team finished first in the Danish U/19 league, which was followed up the next season with another first place. In 2009, he was awarded the “Academy Player Of The Year” award, which is given to players who have excelled themselves during their period at the academy.

He has been a starter in almost all of FC Midtjylland’s games since his arrival at the club. He missed the Danish Cup final against FC Nordsjælland in May 2011 and the UEFA European Under-21 Championship in Denmark due to a cruciate ligament injury. In January 2012 he recovered and rejoined the first team in FC Midtjylland and played all the games in the last half of the season. Prior to the season 2013/2014 he was made vice-captain of the first team.

Due to his dual citizenship, Sviatchenko was eligible to play for Ukraine, but agreed to a call-up for the Danish national team on 25 March 2015, due to injuries for Daniel Agger and Jores Okore. He made his international debut the following day at NRGi Arena in Aarhus, starting against the United States in a 3–2 friendly win, in central defence alongside Simon Kjær.

On 16 January 2016, it was reported that Sviatchenko was in Glasgow undergoing a medical with a view to joining Celtic in a £1.5 million transfer. The transfer was confirmed the following day, with Sviatchenko signing a four-and-a-half year deal with Celtic. Sviatchenko helped Celtic win a domestic treble in 2016–17. He damaged knee ligaments in a 2017–18 UEFA Champions League qualifier against Rosenborg, which prevented him playing for three months. In January 2018, Sviatchenko returned to FC Midtjylland on loan until the end of the 2017–18 season. That loan move was made permanent on 27 May 2018 for a fee of £1m.

His wife, Anne Rudmose, is also a professional footballer and has played for Viborg FF’s women’s team and the Denmark national team. Rudmose signed for the Celtic women’s team in February 2016, one month after Sviatchenko had joined the men’s team.