Yes. Hitler's genocidal intent and deep-rooted antisemitism are extremely well recorded, both in his own writings in Mein Kampf, his numerous speeches, and in accounts of his interaction with others. This post goes into some detail in discussing Hitler's stake in the Holocaust, while numerous other posts in our FAQ also discuss Hitler's antisemitic beliefs.

If your question is referring specifically to the existence of a written order for the Holocaust by Hitler - then no, no such order exists, but its absence frankly isn't relevant or telling to any meaningful discussion of the Holocaust. /u/elos_ explains this in considerable detail here.