Just to add an up-to-date answer, I wrote an App which changes the DNS of both Wifi and mobile connections also without root. Have a look at [PlayStore][1] or [Amazon][2].


  [1]: https://play.google.com/store/apps/details?id=com.aykutcevik.dnssetter&utm_source=global_co&utm_medium=prtnr&utm_content=Mar2515&utm_campaign=PartBadge&pcampaignid=MKT-AC-global-none-all-co-pr-py-PartBadges-Oct1515-1
  [2]: http://www.amazon.com/Aykut-%C3%87evik-Lilly-Setter-Adblocker/dp/B01862KUFI