The 26-year-old centre-back, who moved to Ligue 1 four years ago, was offered a new deal at the Allianz Riviera but has opted to join an unnamed club taking part in continental competition next season.
Speaking to Nice's official website on Wednesday, he said: "I wanted to stay but, in the end, we could not reach an agreement.
"My current ambitions are currently higher that what the club can offer me today. I know OGC Nice can improve and I hope to return one day but, right now, I have to think about myself and my family.
"I have always wanted to play in the Champions League or at least in some other European competition. It is a dream I have had since I was little. I now have the opportunity to do so."
Pejcinovic made 100 appearances for Nice in all competitions but only managed to feature in 15 matches during the 2013-14 season due to a groin injury.
Les Aiglons ended the campaign in a lowly 17th place and avoided relegation to Ligue 2 by only two points.
Pejcinovic added: "I hope I left a good impression of myself here. I thank the fans, and everybody. Nice will always be close to my heart."