rsync over ssh é provavelmente sua melhor aposta com a opção --remove-source-files
rsync -avz --remove-source-files -e ssh /this/dir remoteuser@remotehost:/remote/dir
um teste rápido dá;
[tomh@workstation001 ~]$ mkdir test1
[tomh@workstation001 ~]$ mkdir test2
[tomh@workstation001 ~]$ touch test1/testfile.1
[tomh@workstation001 ~]$ ls test1/
testfile.1
[tomh@workstation001 ~]$ rsync --remove-source-files -av -e ssh test1/testfile.1 tomh@localhost:/home/tomh/test2/
sending incremental file list
sent 58 bytes received 12 bytes 10.77 bytes/sec
total size is 0 speedup is 0.00
[tomh@workstation001 ~]$ ls test1/
[tomh@workstation001 ~]$
[tomh@workstation001 ~]$ ls test2/
testfile.1
Como @SvenW mencionou, -e ssh é o padrão, portanto, pode ser omitido.