In an article on how to stop it, Microsoft has revealed that they will be pushing out the Chromium-based Edge browser to the majority of Windows 10 users.
Microsoft will be pushing out the update, replacing the old Edge, to all Windows 10 users on Windows 10 RS4 (April 2018 Update) and newer.
This may of course cause compatability issues, and Microsoft is releasing a Blocker Toolkit for enterprise users to control the rollout.
To help our customers become more secure and up-to-date, Microsoft will distribute Microsoft Edge (Chromium-based) through Automatic Updates for Windows 10 RS4 and newer. The Blocker Toolkit is intended for organizations that would like to block automatic delivery of Microsoft Edge (Chromium-based) to machines in environments where Automatic Updates is enabled. The Blocker Toolkit will not expire.
For computers running Windows 10 RS4 and newer, the Blocker Toolkit prevents the machine from receiving Microsoft Edge (Chromium-based) via Automatic Updates.
The Blocker Toolkit will not prevent users from manually installing Microsoft Edge (Chromium-based) from internet download, or from external media.
Organizations do not need to deploy the Blocker Toolkit in environments managed with an update management solution such as Windows Server Update Services or System Center Configuration Manager. Organizations can use those products to fully manage deployment of updates released through Windows Update and Microsoft Update, including Microsoft Edge (Chromium-based), within their environment.
The toolkit and more information can be found at Microsoft here.