Yes, roboticus++, you're right, a one-line shell command at the prompt is sufficient for the task at hand.

But not being a great fan of the shell syntax, I would personally tend to do it with a Perl one-liner, something like this (reusing here the OP's syntax):

perl -ne 'chomp; system("cp $_ newdirectory/")' mylist.txt
[download]

even though it might be slightly less efficient, or possibly something similar using the File::Copy module.