6:41 AM PT -- It's official ... but Knicks owner Jimmy Dolan isn't calling it a "firing" -- he's saying both sides have "mutually agreed to part company."

Yeah, right.

"After careful thought and consideration, we mutually agreed that the Knicks will be going in a different direction," Dolan said in a statement.

"Phil Jackson is one of the most celebrated and successful individuals in the history of the NBA. His legacy in the game of basketball is unmatched. We wish him the best and thank him for his service to the Knicks as both a player and an executive."

Dolan says he will not be personally involved in the search for Phil's replacement.

Phil also put out a statement saying, "The New York Knicks will always hold a special place in my heart."

"I had hoped, of course, to bring another NBA championship to the Garden. As someone who treasures winning, I am deeply disappointed that we weren’t able to do that. New York fans deserve nothing less. I wish them and the Knicks organization all the best -- today and always."

The NY Knicks are done with Phil Jackson -- the team is expected to announce he's leaving the organization as early as Wednesday morning.

71-year-old Jackson is the President of Basketball Operations for the Knicks -- and people HATE him right now ... after another terrible season and personality clashes with Carmelo Anthony and Kristaps Porzingis.

Multiple stars have called for the Knicks to fire his ass -- including Kenyon Martin and Fat Joe.

Now, it seems the Knicks are taking their advice ... with ESPN's Ramona Shelburne reporting he'll be out before the day's over.

The Zen.

Spike Lee has already weighed in ... he's happy.