Oliver is expected to announce the new legislation at a lunchtime speech to a business group in Toronto on Wednesday.
The "balanced budget bill" was promised in the 2013 Throne Speech and is expected to only allow for temporary deficits in "exceptional circumstances."
The financial crisis of 2009 would likely have qualified as such a case.
That year the government's budget included a $56-billion deficit — the largest in Canadian history.
A number of provinces have already introduced such legislation before and were eventually forced to either break it or repeal it as economic circumstances changed.
Critics of such legislation dismiss it as a "gimmick" since it can easily be overturned or suspended with a simple majority vote in the House of Commons — the same type of vote that is needed to pass a budget.