As with chord shapes, a great way to memorize a progression is to play it through all the keys in the key cycle. Here is a II V I progression played anti -clockwise around the cycle. Once you are comfortable with it, try playing the progression clockwise around the cycle.
As well as using the key cycle, try playing a chord progression in one key and then move through other keys by starting the progression up or down by a specific interval, e.g. chromatically (minor 2nds), major 2nds, minor 3rds or major 3rds. If you make a habit of this, you will soon be able to play a progression in any key. This will make you popular with other musicians because it saves a lot of time at rehearsals.