"I have made the decision to try something new after this season and to leave the club. It was a difficult decision. I have been here for 13 years. I made so many memories here," Alaba said, according to ESPN FC's Stephan Uersfeld.
"I have not decided what is next for me. I decided to seek a new challenge. That's why it took time. ... I have five, six, seven years left in my career. That's why I decided to try something new.
"It's no secret my management is in touch with several clubs. I will focus on my task here and will remain in contact with my management."
Alaba's departure was widely expected after he failed to reach an agreement with Bayern over a new contract. In recent months, he's been heavily linked with a move to Real Madrid.
The versatile 28-year-old, who is capable of playing in central defense, left-back, and even in midfield, reportedly accepted a four-year contract in January to join Real Madrid on a free transfer this summer.
Alaba is fresh off helping Bayern capture their sixth major trophy in a year after winning the FIFA Club World earlier this month.
The Austrian international has won nine Bundesliga titles, two Champions League trophies, and dozens of other major awards since joining the Bavarians in 2010.