I managed it a few years ago.
Just sort out utorrent with the folder name etc and transfer the files to your new PC (or plug in the HDD or whatever) and then double click the original torrent files.
If it's done right, Utorrent will check the files and start seeding them.
The thing is, you must tell Utorrent where the files are and restart the torrents.
If you get "downloading" instead of "checking", you've pointed it to the wrong place.
As your copy of Utorrent will be a new one, it won't have any memory of the files you have already downloaded regardless of where they are so they all need to be restarted again.
Example:
Point to folder, say, C:/Utorrent files as where to save the files to (or, if on an external, to where they are now).
Move all the files you want seeding to that folder on your new PC (no action needed if on an external that you used with the last PC).
Find the original torrent files you downloaded (download them again if you deleted them) and double click on them to start them.
Utorrent looks in the folder you specified and, if it finds the file already there and unchanged, it will just check all is OK and start seeding.
Long winded but it worked.
Of course, now someone will come along with an easier way ;D