The Danish international, who played 63 times for Celtic, was signed by Ronny Deila in 2016, but struggled with injury and spent the second half of the 2017/18 campaign on loan at his former club where he won the league title.
During his time in Glasgow, Sviatchenko won two Scottish Premiership titles, two League Cups and one Scottish Cup, and was part of the “Invincibles” team that went through the 2016/17 campaign undefeated under Brendan Rodgers.
A club statement read: “Everyone at Celtic would like to thank Erik for his contribution to the club’s success over the past two-and-a-half years, and we wish him every success in the future with FC Midtjylland.”
In an emotional statement posted on Twitter, Sviatchenko wrote: “I am forever grateful to the club for giving me some of my biggest experiences as a football player.
“The highs have been amazing and unforgettable. I will be able to reflect upon two years with pride and admiration.
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“I am an “Invincible” and I did it with some amazing team maets, coaches, staff and the world’s best fans.
“I have won many trophies and have been a member of one of the most iconic clubs.
“A special thanks to Ronny Deila for bringing me to the club and to Brendan Rodgers for helping me develop and become a much better player.
“Celtic isn’t just a club it’s a family and one that I’m utterly proud to be a part of and to have contributed to.
“I have given my heart and soul and I’ve felt the same towards me from all of the supporters.
“Not many players will experience a Champions League campaign and I am so proud to be a part of a squad who played against world class players.
“My family and I will always remember Glasgow and Scotland as something fantastic. The people are genuine and have always helped us when needed.
“Wish you all the best and we might see each other soon again.”