The Ligue 1 club confirmed the arrival of the 25-year-old left-back on their official website on Monday.
He is set to be introduced to the media on Wednesday after passing a medical.
Juelsgaard moves to France after several seasons of regular first-team action at Midtjylland.
He has also made two appearances for his country, the most recent as a second-half substitute in March's friendly defeat to England at Wembley.
Evian finished 14th in Ligue 1 last season, after beating Sochaux on the final day of the season with relegation still a possibility.