tmux needs help from xsel (or another X clipboard manager).
I use xsel and add this to my ~/.tmux.conf, which will allow CTRL+B CTRL+C (copy) and CTRL+B CTRL+X (paste) to/from the X (PRIMARY) clipboard into the tmux selection buffer (and vice versa).
# turn on clipboard
set -g set-clipboard on
# copy tmux's selection buffer into the X clipboard selection
bind-key C-c run-shell "tmux show-buffer | xsel -b -i" \; \
display-message "Clipboard buffer copied to xsel ..."
# copy X clipboard selection into tmux's selection buffer
bind-key C-x run-shell "xsel -b -o | tmux load-buffer -" \; \
display-message "Clipboard buffer copied from xsel ..."