Purchased licence for Windows and changed to an Apple device

Dear Community,
I have recently purchased an MacBook. Before that I was using a Windows computer and purchased licences for CS6 and Lightroom 4 (quite some time ago).
I am aware that I (might) have to buy them new to use them on my new laptop, but I read different information about it and that it might be possible to use them still via contacting the support and following an upgrade.
Does someone know how the procedure works for that or if I really have to purchase it completely new.

Thanks in advance!