You're account (if you are talking about my.avast.com) isn't system specific ?
If you are talking about your avast 'license' (avast Pro and avast Internet Security only) ?
Then your license can be used and is valid on the new computer. Provided that it is a multi PC license or you subsequently uninstall the copy on the old computer, so you don't have it actively installed on more PCs than the license is for.
