SQL Server 2016 Developer's Guide

Enabling Stretch Database

Before you select some tables for stretching, you need to enable the feature on the instance level. Like many other new features, it is disabled by default. To enable it, you need to execute the following statements:

EXEC sys.sp_configure N'remote data archive', '1'; 
RECONFIGURE; 
GO 

Actually, you have to allow remote data archiving; there is no enabling Stretch Database option. Anyway, after enabling it on the instance level, you can choose a database and enable the feature at the database level.

Enabling Stretch Database at the database level

If the feature is enabled at the instance level and you have enough database permissions (db_owner or CONTROL DATABASE), the next step is to enable Stretch DB at the database level. ...