Yes you can.
Assumption: this is your only internal HD in the new PC.
In order for this to work, you will need to do one of the two following.
Option 1: have a license for everything you need to install (including the OS) and a 2nd PC to potentially download drivers as they might not be included with your new OS (they have a limited number of included drivers which can't include every odd bit of hardware).
Option 2: make an image of the current HD and drop it on your new SSD. The easiest way to do this is to use a 2nd PC. Remove the current HD from your new laptop, place it in an external HD holder, use a tool to make an image of this HD such as Acronis (there are many choices, use your favorite), put the SSD in the external drive...