It's straightforward - unlike Windows user accounts are very simple. If you are using local accounts then a user account is just a line in three files (/etc/group, /etc/passwd, /etc/shadow), a home directory and probably a mailbox file in /var/spool/mail.
You can copy the lines that relate to the user accounts from the three /etc files in the old system to a copy of the files on the new system. Then replace the files on the new system with your edited versions.
Then create home directories, transfer the files with SSH, and reset permissions. You can write a shell script to do these.