Note: this was originally a lot longer and more complex, but a later version of tmux show-environment supports formatting the output as shell commands to eval, so this is much easier now.

tmux is a tty multiplexer similar to screen, but with some really nice features. One of those features is updating environment variables when you reconnect to a session - the client sends the current values to the tmux server, and they can be retrieved with:

$ tmux show-environment -s
unset DISPLAY
SSH_AGENT_PID=3912; export SSH_AGENT_PID
unset SSH_ASKPASS
SSH_AUTH_SOCK=/tmp/ssh-lXpzMY3205/agent.3205; export SSH_AUTH_SOCK
SSH_CONNECTION=192.0.2.1 43512 192.0.2.1 22; export SSH_CONNECTION
unset WINDOWID
unset XAUTHORITY

Of course, tmux can’t force other processes to update their environment. bash has a hook you can use to do it: PROMPT_COMMAND. If this variable is set to the name of a function, bash will run that function before displaying your prompt. Here’s a function and supporting settings to update your environment:

function prompt_command() {
  if [ -n "${TMUX}" ]; then
    eval "$(tmux show-environment -s)"
  fi
}
PROMPT_COMMAND=prompt_command