As you're already using it, I'd recommend tmux as fully supports copy and paste - see the manual page for more information.
You can see the current key bindings by using the tmux list-keys command - look for the begin-selection, copy-selection and paste-buffer commands in that list.
By default, the bindings are:
- [ - Start copy/paste mode
- h, j, k, l -
vi navigation keys to move the cursor
- v - Start text selection (once selected, hit Enter to copy to the buffer for later pasting)
- ] - Paste copied text
There are some limitations when using it with a curses-based application like vim (as tmux can't then manage scrolling) - you're not able to scroll back to previous output.
As an alternative (and if you're only copying between vim sessions), you can use a temporary file as a clipboard (you'll need to do this if you're not using X11). See this post suggested by @muru for further information.