Microsoft Edge is finally getting the History and Open tabs sync feature with Chromium Edge version 88. As the feature is currently rolling out to a limited set of Edge Insiders in the Canary channel, you can now see the options to enable the sync if you are one of the lucky users.
The feature is currently rolling out for Windows, and Mac users. Upgrade to Edge Canary build 88.0.682.0 or higher to check if it has been enabled for you.
With this history and open tabs sync support, you can now access currently opened and visited web pages across your devices. Once it released to the stable release channel, all users will be able to access the improved sync feature of Microsoft Edge (Chromium).
UPDATE 05-January-2020:
Microsoft started rolling out the History and Open Tabs sync feature to the Microsoft Edge stable release channel.