If you've got the original discs or links to where you downloaded the software – along with any serials, of course – then there's no reason why you can't install the apps on your new computer. Of course, if you use Time Machine or migration assistant to transfer stuff from your old Mac to your new one then you'll be able to transfer your apps this way.
The only real issue is are you going to be using two Macs or are you selling your old one? If you're keeping both, then check out the licence for your apps as many have limits on the number of computers they can be installed on.