The company said people will begin seeing BBM available on Monday, but UAE users do not yet have a specific roll-out date.
BlackBerry rolls out BBM for Android and iPhone users
BBM, or BlackBerry Messenger, is an application that allows text messages and pictures to be sent for free to other users who have also downloaded it, much like the popular messenger Whatsapp.
"In the next few hours, people will start seeing BBM in Google Play, the App Store and in select Samsung App Stores - where it will be free to download," the company said in a blog post on its website on Monday.
BBM was previously only available on BlackBerry's own mobile handsets.
BlackBerry said on Monday that given the high demand for downloads a "line-up" system is being rolled out worldwide.
It said that the easiest way to gain access to the service is to visit bbm.com on any Android device or iPhone and install the app.
Users who sign up on the website will then receive a notification via email telling them when the service is available.
The post on the BlackBerry website stated that those who had previously signed up will be able to immediately start using the service.
Updates on the progress of the rollout will be posted on the company's twitter feed @BBM.
It is unclear when precisely UAE users will be able to use the app.