With only this one symptom I will give you the most obvious answer. If you reply with more symptoms we can better reply. Now is this an itch, or tingle like your limbs are going to sleep, which means they are lacking blood circulation?
Assuming itch as you said, can we say that you are not shaving your legs in the shower? If so, I would venture that you did not scrub your legs with a wash cloth. If this is true, try doing this every bath and removing dead skin cells that will otherwise cause this itch as they dry.
If you already scrub, this might be an allergy to your current soap. Is the brand you are using some what new? If so, change to Dial, irish spring, or some other brand that does not leave a residue.
Then if you are using a new skin cream, try not using it for a few days to see if this eliminates your itching.
Now if you do scrub and you have not changed your soap in forever and you do not put on lotion then get a good body lotion and put this on your legs after every bath. It will take a few times if it is the lack of skin moisture.