Yes you can. You can buy any ssd and put it in place of the hdd OR you can keep the hdd and remove your DVD tray and replace it with a SSD.
I also have a HP Envy. I will be replacing my DVD drive with a SSD soon. I have to buy a bay for the SSD but it should be fairly easy.
When you add a SSD to your computer it is better to do a fresh install of Windows on your SSD.