The 26-year-old spent the second half of the 2017-18 campaign with the Wolves and has now rejoined on a full-time basis.
Sviatchenko leaves Parkhead after winning two Scottish Premierships, two League Cups and the Scottish Cup, making 63 appearances in all for the Glasgow giants.
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."
Sviatchenko added: "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."