Yes, you will need Veracrypt available on the computer in order to access the drive. However, you don't need Veracrypt installed. There is a portable version available for both Linux and Windows.
If you have Veracrypt available on all machines in question, you can keep it simple and have the whole drive encrypted.
However, you can also bring the portable versions with you on the same drive: Make a normal (unencrypted) partition the size of the whole drive. (ex-FAT if you want it to work on both Linux and Windows) Then have the portable verion(s) of the program on it as well as a Veracrypt encrypted container file. The encrypted container will be a big, unreadable file on the drive that will require your password to unlock and use. Then store the rest of everything inside the encrypted container.