I think that the only thing that really works are code reviews. The best engineers on the team should have enough time to review what is being committed and provide suggestions for improvement. Things will start gradually improving, but it usually takes a very long time before you see any progress.
Like someone already mentioned in this thread before, an important part of this transformation is to not forget about the political aspects of such cleanup process. People don't like to hear criticism, so you will probably encounter a lot of pushback in the beginning.
Like someone already mentioned in this thread before, an important part of this transformation is to not forget about the political aspects of such cleanup process. People don't like to hear criticism, so you will probably encounter a lot of pushback in the beginning.