Ljungberg and head coach Andries Jonker were sacked by Wolfsburg this week.
In a statement posted via his official Twitter account, he said: "While it's disappointing to have left VfL Wolfsburg less than a year into our project I can look back on my time there with great pride.
"I am lucky to have worked with talented players and been supported by a passionate and loyal fanbase who played a significant role in our Bundesliga survival.
"It's a shame that, after just four games this season and sitting joint 12th [14th on goal difference], the club have decided to change the head coach, Andries Jonker, but this is modern football.
"Although I may disagree with it, I respect the board's decision and am sad to be leaving VfL Wolfsburg; I thank the club for the opportunity they gave me and look forward to my next challenge."
Former Mainz boss Martin Schmidt has been appointed as Wolfsburg's new head coach on a two-year deal.