We had the same issue today. It turned out to be a permissions issue, as illustrated in some of the other answers. The difference is that the account we needed to add was NT SERVICE\MSSQLSERVER.

I identified the account by comparing the permissions of the default SQL Backup folder permissions to the folder containing the backup file.
Adding the service account is not as simple as it sounds. Here is what worked for me (Server 2012 R2). The official MS docs are here.
- Log into the server. (The change must be made on the actual server, not through a network share.)
- Change the Locations to the local server name.
- Type in
NT SERVICE\MSSQLSERVER in the name box. (Do not click Check Names). If your SQL SERVER has a set instance name (i.e., you are connecting to MyComputer\[SQLSERVERINSTANCE]), enter NT SERVICE\MSSQL$[SQLSERVERINSTANCE] instead, (where [SQLSERVERINSTANCE] is replaced with your actual instance name).
- Click OK. You will then see a list of the matching service accounts. Select MSSQLSERVER, and click OK to accept the selection.


You should see the service account listed in the security settings, and can adjust the permissions accordingly.
After adding permissions (I added Full Control, to match the default SQL Backup folder.) and restarting the SQL Server Management Console, I was able to select and restore my backup file.