Users will be able to control where they receive messages and calls - in their chats, through message requests, or disable the feature entirely.
The change means that Instagram messages will receive multiple features already available to Messenger users, including a vanish mode where messages will disappear after sending, similar to Snapchat, personalising messages with colours, and quick-forwarding.
It will also allow Instagram users to use the Watch Together feature that is available in Facebook Messenger, to view Facebook Watch, IGTV, TV shows, movies, and other content.
Mark Zuckerberg has in the past suggested that the plan is part of a vision for the future of Facebook as a private social network.
Just like today you could talk to a Gmail account if you have a Yahoo account, these accounts will be able to talk to each other through the shared protocol that is Messenger, Loredena Crisan, VP of Product Design for Messenger, told Engadget.
More than a billion people already use Messenger as a place to share, hang out and express themselves with family and friends.
However, various commentators have pointed out that bringing the apps together could help improve the fortunes of Facebook amid criticism, and that it would make it harder for regulators to attempt to break the company into its various constituent apps.
Facebook first purchased Instagram because the photo-sharing platform could hurt the company, emails from Mark Zuckerberg during an antitrust hearing revealed.
Currently, the update is rolling out in a few countries around the world but Facebook says that it will expand globally soon.