With August 2015 CU for SharePoint 2013 Microsoft added cloud hybrid search capability to SharePoint Server 2013.
With cloud hybrid search, you index all your crawled content, including on-premises content, to your search index in Office 365. When users query your search index in Office 365, they get search results from both on-premises and Office 365 content.
For more information about cloud hybrid search, including how to configure it, you need to join the Microsoft® cloud hybrid search preview program.
After you have joined the program you can use the following link to access the documentation for the cloud hybrid search feature: https://connect.microsoft.com/office/program8647.
Be aware that August 2015 CU for SharePoint 2013 contains the required changes for SharePoint 2013 to enable this feature. The hybrid search functionality itself will be available as a preview in Microsoft Office 365 starting on September 7, 2015.
KB 3080169 – Cloud hybrid search capability in SharePoint Server 2013