Stoke boss Mark Hughes was anxious to land the 34-year-old striker, and had held talks with him about a summer switch to the Britannia Stadium.
But, despite Olic expressing a desire to try his hand in England, he has opted to remain with his current club Wolfsburg and has signed a two-year extension.
"I am very happy that now I have clarity about my future and that I will continue to play at Wolfsburg," Olic revealed.
"We want to attack fully in the Bundesliga and in Europe in the coming season.
"It gives me an incredible amount of fun to be part of this team and my family feels very comfortable here."
Olic has scored 13 goals in the league so far this season and Wolfsburg are happy with his decision.
"When a player like Ivica Olic, who is attracting the attention of clubs at home and abroad, decides to continue his career here in Wolfsburg, then that shows that we are convincing our players with the direction we want to go in," said the club's director of sport Klaus Allofs.
"His contract extension is another important piece in the puzzle which is our preparations for next season, and beyond."
Coach Dieter Hecking was also delighted by Olic's decision, saying: "There's nothing more that really can be said about his quality. He is hugely important for our young team, not just because of his great experience."