To add to Jefromi's answer, if you don't want to place a meaningless merge in the history of the source branch, you can create a temporary branch for the ours merge, then throw it away:
git checkout
git checkout -b temp # temporary branch for merge
git merge -s ours # create merge commit with contents of
git checkout # fast forward to merge commit
git merge temp # ...
git branch -d temp # throw temporary branch away
That way the merge commit will only exist in the history of the target branch.
Alternatively, if you don't want to create a merge at all, you can simply grab the contents of source and use them for a new commit on target:
git checkout # fill index with contents of
git symbolic-ref HEAD # tell git we're committing on
git commit -m "Setting contents to " # make an ordinary commit with the contents of