The company said that the update for other Galaxy devices "will soon follow" but said that details of the upgrade schedule would depend on the "market situation and carriers' requirements".
As part of the Marshmallow update Samsung is also updating the 'edge screen' feature of the S6 Edge, making it bigger, stretching it from 260 pixels out to 550 and giving users the option of adding more apps.
Photos: Android through the ages
Android Marshmallow - a major update to Google's mobile operating system - was unveiled back in September last year, showcased on the Nexus 5X and Nexus 5P. Noteable new features include Google Now on Tap which displays relevant information based on what an app is showing on screen, and the ability to manage privacy permissions more carefully.
But adoption has been slow: as of the start of the start of February Marshmallow was being used on just 1.2 percent of Android devices (up from 0.7 percent in January), with KitKat remaining the most popular version. However, manufacturers are gradually announcing they will roll out Marshmallow, and Samsung kicking off the upgrades on its flagship phones will see adoption accelerate rapidly.
The news of the upgrade comes just days before Samsung is expected to unveil its latest high end smartphone, the Galaxy S7.