With a vocabulary of 23500 German words and phrases, you should be able to understand in excess of 99% of what you read in German newspapers (provided, of course, that your knowledge of German grammar is adequate for newspaper texts).
I did a little research to come up with the above percentage.
Because I write out nearly all unfamiliar German words and phrases** from German newspapers into my German-English wordlist, I know almost exactly the size of the German vocabulary I’ve learned. In early July 2016, it constituted 23500 words and phrases. Since then I have read 100 articles in different German newspapers (Der Spiegel, Süddeutsche Zeitung, Frankfurter Allgemeine Zeitung and others). The total length of the articles is 63687 words. Of these, as it turned out, only 333 words and phrases were new to me (0,5%).
Sometimes, if you don’t know a word or a phrase, the entire sentence or paragraph in which it occurs, may not be understood, which would drive down your understanding of the text from about 99% to a lower percentage. This should at least partially be offset by your being able to understand quite a few German words that you have not learned, but still recognize (e.g. from context, from the semblance of a German word you haven’t encountered before to a similar word in your native language etc.)
** To clarify what I mean by "words and phrases", here are some examples: die Biegsamkeit, belehren, packend (words); einen Rekord aufstellen, jdn. von etw. abbringen (phrases).