Stephen Colbert has finally locked in the end of "The Late Show" ... with the curtain set to fall for good on May 21, closing out a CBS late-night run that’s lasted more than 30 years.

Stephen broke the news during a taping of "Late Night With Seth Meyers" on Monday ... officially putting a date on the farewell that’s been looming since last summer.

Remember, CBS and parent company Paramount Global announced plans to cancel the show back in July, blaming straight-up financial reasons.

But the move raised eyebrows, as it followed Colbert publicly slamming Paramount for settling Donald Trump’s "60 Minutes" lawsuit ... calling it a "big fat bribe" from the company.

But, his TV monologues might not be done for good -- 'cause he’s already joked about wanting a job at TMZ ... and yeah, we’ve got the receipts!