TMUX using HJKL to navigate panes

You can do this as follows:

bind h select-pane -L
bind j select-pane -D
bind k select-pane -U
bind l select-pane -R

Note that mode-keys refers to using vi-like navigation within a buffer and status-keys refers to using vi-like editing within the status bar, but neither refers to switching between panes.

Did you remember to source your ~/.tmux.conf file? After making any changes in this file you need to enter the following command to see any of the changes take place

tmux source-file ~/.tmux.conf

The Micah Smith's answer seems to work. But it doesn't have quite the same behaviour that we have with the arrow keys. With the arrows, if you are fast enough, you can hit prefix + arrow key multiple times and you are able to navigate multiple panes, using the same prefix hiy. Main difference:

With the arrows:

// to move 3 panes to the right
prefix + -> -> ->

With this hack:

// to move 3 panes to the right
(prefix + l) 3x

Still, to make this change, you need to update your ~/.tmux.conf file and then restart tmux sessions. To be sure you don't have any tmux sessions you can run

$ tmux list-sessions

If you have some sessions running, run $ killall tmux and you should be good to go.

This☝️ was tested in a macbook, it should be the same for linux.