How to replace master branch of a repo with that of another totally unrelated repo?

Hello,
I want to rewrite a program totally from scratch rather than branching
from current one.
So I created a new repo for it and do the development there.
Now it's finished and I want to replace the old program with it.
Is it possible to replace the master branch of the old repo with the
code in this new repo?
I want to move the old code to a separate branch for backup, and
replace the master branch with the master branch of the new repo.
Since git rm -r * than git add all new files will lost history of new
repo, it's not an option.
The old repo is a public online repo used by multiple users. So just
renaming the repo won't work since the users who pull code from the
old repo will get troubles.
What's the best strategy for smooth migration in this case?
I'm not able to find the answer on Google.

Thank you all.