I have old Software Center history and I would like to clear it all.
I tried
sudo rm -rf /var/log/apt/history.log /var/log/dpkg.log
but it did not work.
You were close—Software Center just keeps a cache of the APT history in your home folder. If you need to wipe it:
Delete the APT history log, /var/log/apt/history.log*
. (Don't forget the rotated log files.)
Delete the Software Center's pickled cache, ~/.cache/software-center/apthistory.p
, from every user's home folder.
I'm not sure why your question was down-voted.
rm -rf
... but anyways, do you really know where the software center logs?