A drive has to have at least one partition in order to be formatted. The partitioning step determines the type of partition map that will be created on the drive [GUID, MBR (master boot record), or Apple Partition Map (rarely used)]. You will want to ensure that the drive is using a GUID partition map - whether there will be a single partition or multiple partitions. If the drive currently has a GUID partition map and only one partition (basically the one partition is the entire drive) - then all you need to do is erase the drive. However - it is simply easier to just "erase" at the drive level and respecify GUID Partition Map and OS X Extended Journaled for the format. This will create a single partition consisting of the entire drive.
Connect the drive and open disk utility.
In the side bar select the external drive itself (the outdented one with the mfg name on it).
Click the Erase Tab (The erase tab is the only place where you can change the partition Map scheme to GUID)
Specify GUID partition Map - Format: OS X Extended Journaled - Provide a name for the partition - otherwise it will default to untitled.
Click erase. The erase process should take less than one minute.
The drive can now be used. It will show up as a single drive/volume comprising all available space on the drive.
You can then drag and drop your Photos Library to the external drive. This will copy rather than move the library. After successful copy and verification of the photos library on the external drive - you can then delete the library from the internal drive.
Keep in mind that your Photos Library on the external drive will no longer be backed up by Time Machine - because the external drive will be excluded from the Time Machine backup process (you can go into Time Machine settings and tell it to include the external drive). You need to ensure that you have adequate backups of the Photos library elsewhere in case the external drive fails.
~Scott