Specifically, the services that will run on Microsoft's cloud solution are Creative Cloud, Marketing Cloud, and Document Cloud.
Adobe Marketing Cloud will also be Microsoft's "preferred marketing service" for Dynamics 365 Enterprise Edition, a service that was also talked about today at Ignite. That service is slated to arrive in 2017.
It's not the first time that Adobe has partnered with Microsoft when it comes to cloud services. In April 2015, Adobe announced that Marketing Cloud Solutions would be running on Azure, and that Campaign and Experience Manager were already using the service.
The partnership is the latest in an attempt to compete with the likes of other cloud service providers, such as Google and Amazon. Microsoft has been trying to emphasize its strengths over its competitors, such as hybrid cloud and of course, its strategic partners that are using the services.