According to BBC Sport, Celtic had to pay a transfer fee of in the region of £1.5m to secure the services of the Denmark international.
Sviatchenko has taken to social media to express his delight at joining the Hoops and has thanked his former club Sviatchenko.
Celtic are at the top of the Scottish Premiership table at the moment with 49 points from 21 matches.
The Glasgow-based club are three points clear of second-placed Aberdeen, who have played a game more, and are on course to winning the league title yet again.
Ronny Deila’s side will take on Hamilton Academical at Celtic Park in Glasgow in the Scottish Premiership on Tuesday evening.