There are three answers to that question:
1) Yes, normally it's doable.
2) Yes, but with some limited functionality.
3) No, it won't work.
But which of the three answers above will apply will depend on the type and age of the software you are trying to install.
But rather than bother with old versions of software, grab the latest version of the software you want to install so that the application software and the operating system of your new computer are compatible — compatible meaning that the application software has been developed to work with specific versions of an operating system, so double-check that the software you want to install is compatible with the operating system of your new computer.
For example, Software 10 will work with Operating System 10 perfectly, but, Software 10 may not work with Operating System 9, because Operating System 9 is older than Operating System 10.