Azure Cosmos DB is available in all Azure regions

This is by default.  In a new region, if Azure opens business, you can associate a Azure Cosmos DB with your account (barring Geo-fencing regions) and new regions are constantly coming on line.

Here are the present and up coming Azure regions:

Globally distributed Azure Cosmos DB

This is how Azure Cosmos DB is described by Microsoft,

"Azure Cosmos DB is Microsoft's globally distributed, multi-model database. With the click of a button, Azure Cosmos DB enables you to elastically and independently scale throughput and storage across any number of Azure's geographic regions. It offers throughput, latency, availability, and consistency guarantees with comprehensive service level agreements (SLAs), something no other database service can offer"

If you are looking for Global Distribution, horizontal scaling, guaranteed latency, high availability, comprehensive SLA's and unrivalled Data Model and APIs that no RDBMS, no no-sql database can provide, there is nothing out there to match Azure Cosmos DB.

Azure Cosmos DB Engine supports multiple database systems and it is based on the following:

 Atom: Consisting of a small set of primitive types (String, Bol, number)
 Records: Structs
 Sequence: Arrays of atoms, records and sequences

Azure Cosmos DB engine currently supports the following:

Document DB SQL
Mongo DB
Azure Table Storage
Gremlin Graphh Query API
It will support other API's in the future.

For developers looking for a globally distributed database system Azure Cosmos DB is the answer.