While Amazon says that Apple Music will work with echosmiths starting in the week on December 17, it does not say how fast the rollout will go, so echo owners may need to be a little patient. When Apple Music is ready to go, it can be activated in the Alexa app like any other skills.
This selects only the second voice-controlled speaker to work directly with Apple Music, according to Apple's own HomePod. Amazon's language in the blog post makes it clear that this feature will only work with echolytters, but other devices that use Alexa as Sonos One will probably not get this extra functionality.
This new partnership follows the news that many more Apple products (including the new iPhones, iPads and Apple Watch) will be available for sale on Amazon this high season. Similar to that, adding Apple Music to the Echo-based is simply a pragmatic business decision. Apple Music has many users and support for great services as it will only lead to happier echo owners.