It's possible with the use of Automation Studio.
Depending on your use case, you could write a SQL query to join data from the two data extensions based on predefined criteria and populate the results into a Shared Data extension. This SQL query could be then automated and scheduled, for example, to run every day or every hour, or - since you mentioned Synchronized Data Extensions - even every 15 minutes, to ensure the latest data gets populated.
If you're Synchronized Data Extensions contain a large amount of data, you should also consider performance when setting up this automation.