Most developers are hesitant to accept new programming paradigms, so it takes a very long time to change how people write code (something Brett Victor captured brilliantly in his talk, The Future of Programming [1]). Therefore, I can't really say if "ten years from now" is the right time frame or if it's more like thirty years.
That said, I think it's safe to say that static typing is "winning" if it ends up being used in almost every single one of the top 10 programming languages. By "used", I mean it's used in the vast majority of the core language libraries and by most major companies that depend on the language. Depending on which popularity chart you want to believe (e.g. langpop [2], TIOBE [3], or RedMonk [4]), the top 10 languages are roughly the various flavors of C (C, C++, C#, Objective C), Java, PHP, JavaScript, Python, Ruby, Perl, and Shell. With the exception of Perl (which will not be in the top 10 for much longer) and Shell (which will probably be in use for a long time), all of those are already statically typed or moving towards it.
I think a similar metric could apply to functional programming: if the top 10 languages use functional programming in the vast majority of the core libraries and by most major companies, then it has "won". This will likely take longer than static typing, but if companies keep adopting languages like Scala and Clojure, they may crack the top 10 some day.
Of course, it's worth mentioning that what's really "winning" right now is a hybrid model: a mix of static and dynamic typing and a mix of imperative and functional programming. Perhaps, in the long term, we'll find where each type of approach works best, use them side by side, and they'll both "win".
[1] http://vimeo.com/71278954
[2] http://langpop.com/
[3] http://www.tiobe.com/index.php/content/paperinfo/tpci/index....
[4] http://redmonk.com/sogrady/2015/01/14/language-rankings-1-15...
