The house where Michael Jackson died is in escrow and about to close ... TMZ has learned ... and the buyer was so anxious, he's moving in weeks before escrow is scheduled to close.

The buyer is Steven Mayer, a super-rich investment banker.  

Our sources say the purchase price was somewhere between $17 and $20 mil -- it was listed for nearly $24 mil.

And this is interesting ... for some reason the seller is letting Mayer move in before escrow closes  -- something real estate honchos think is high risk.

Mauricio Umansky at The Agency represented Mayer and the seller of the home. We reached out to him, but haven't heard back.

At any rate, Mayer loves the crib a lot.  We hope he has better luck than Michael.