You can do this with tmux too.
~/.tmux.conf:
# export to clipboard.
bind-key > run-shell -b 'tmux save-buffer - | xclip'
# paste from clipboard.
bind-key < run-shell -b '( xclip -o | tmux load-buffer - ) && tmux paste-buffer'
(edit: my actual setup is slightly different. It interacts with a Windows clipboard via ssh where the terminal is running. cf. https://github.com/euske/pyrexecd/blob/master/tools/tmux.con... )