The firm said that the app will be free on both operating systems, providing the devices are running at least iOS 6 or Ice Cream Sandwich (Android 4.0).
"You might ask the question why is Blackberry doing this now," said CEO Thorsten Heins, when speaking at BlackBerry Live.
“It is a state of confidence. The BB10 platform is so strong and the response has been so good that the time is right for BBM to become an independent mobile messaging platform.”
The move will at first see BBM only usable for messaging and group features on third-party operating systems, although Heins has said that screen sharing, BBM voice and BBM channels — a new social networking tool — will be coming soon.
The news represents the latest sign that BlackBerry is waking up to today's multi-platform, bring-your-own-device (BYOD) era where the locked-down "walled garden" approach only continues to succeed at Apple.
Back in March, the firm revealed that BlackBerry Secure Work Space, its service for separating personal and work data, would launch on Android and iOS.