I replace tons of those Irritrol Rain Dial controllers. They are simple and easy to transfer to a Rachio controller just as @DLane pointed out.
I also noticed that you have an auxiliary pump on there and your Rachio 3 controller has a terminal for that too.
Welcome to the Rachio community. We are loaded with many professional and experienced irrigation people that can guide your comfortably through a painless installation.
That does look like the outdoor version of the Irritrol controller. If you are installing outdoors, don’t forget to get the original Rachio outdoor box.