The "Database Project" project type in Visual Studio is for database schemas (stored procedures, table definitions etc.). Your SSRS reports should be in a "Report Server Project".

Do you have a Team Foundation Version Control/TFS server? Which version of Visual Studio do you use? Do you have "SQL Server Data Tools - BI" installed so you can see the "Report Server Project" type (under Business Intelligence) in the Visual Studio "New Project" window? If you've just got "SQL Server Data Tools" (which I think is the case from your post here), I don't think you will be able to see the "Report Server Project" type.