The simplest way is to use The BFG Repo-Cleaner, a faster, simpler alternative to git-filter-branch
designed specifically for removing large files from Git repos.
You should follow the usage instructions carefully, but the main step is just this - download the Java jar (requires Java 7 or above) and run this command:
$ java -jar bfg.jar --strip-blobs-bigger-than 100MB my-repo.git
Any blob over 100MB in size will be totally removed from your repository's history - unless it is the version present in the file tree of your latest commit, so your latest version will be untouched, as you required.
The BFG is also 10-50x faster than git-filter-branch
.
Full disclosure: I'm the author of the BFG Repo-Cleaner.