It's very simple. Git doesn't care about what's the name of its directory. It only cares what's inside. So you can simply do:

# copy the directory into newrepo dir that exists already (else create it)
$ cp -r gitrepo1 newrepo

# remove .git from old repo to delete all history and anything git from it
$ rm -rf gitrepo1/.git

Note that the copy is quite expensive if the repository is large and with a long history. You can avoid it easily too:

# move the directory instead
$ mv gitrepo1 newrepo

# make a copy of the latest version
# Either:
$ mkdir gitrepo1; cp -r newrepo/* gitrepo1/  # doesn't copy .gitignore (and other hidden files)

# Or:
$ git clone --depth 1 newrepo gitrepo1; rm -rf gitrepo1/.git

# Or (look further here: http://stackoverflow.com/q/1209999/912144)
$ git archive --format=tar --remote=<repository URL> HEAD | tar xf -

Once you create newrepo, the destination to put gitrepo1 could be anywhere, even inside newrepo if you want it. It doesn't change the procedure, just the path you are writing gitrepo1 back.