OFFICIAL: Sviatchenko rejoins former club Midtjylland on a permanent basis
The Dane joined the Scottish champions from Midtjylland in January 2016, but rejoined his former side on loan in January of this year, helping them to claim the Danish title.
Sviatcheko was part of the Celtic side that finished the 2016/17 season unbeaten, starting 23 league games and featuring in 43 matches in all competitions.
However, he later fell down the pecking order under Brendan Rodgers, ultimately paving the way for his exit.
A Celtic 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."
The 26-year-old was delighted with the move, saying: "I'm proud and pleased that FC Midtjylland have shown that they really want me.
"The club has modelled me both as a human and football player, and in the same way I have tried to give something back both as a human and football player.
"We are entering an exciting time and I am looking forward to being part of an environment that rests on many of the values I also hold."
Sviatchenko made 63 appearances for Celtic, winning two Scottish Premierships, two League Cups and a Scottish Cup during his time in Glasgow.