Lenny Dykstra is fighting Bagel Boss Guy ... yes, the baseball legend inked a deal to box the guy who lost his mind in a NY bagel shop.

We broke the story, Bagel Boss Guy -- aka Chris Morgan -- signed a deal to fight in Damon Feldman's Celebrity Boxing promotion ... only question was, who was he gonna fight?

Now we know ... 56-year-old 3x-MLB All-Star and World Series champ Lenny Dykstra.

We're told Lenny agreed to a deal and signed the contract on Friday (he'll be paid a fixed amount of money for the fight) ... and will begin training immediately for the September 7 bout in Atlantic City, NJ.