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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.

Sources close to Lenny tell us he ain't worried about the lack of time to prepare ... and is very confident he's gonna beat the hell outta BB Guy.

If he does ... it won't be cause Bagel Boss ain't training hard for the scrap.

Morgan recently went to one of the best MMA gyms in the country ... and training with UFC superstars Al Iaquinta and Chris Weidman.

In fact, Iaquinta told us Morgan possessed some natural ability as a fighter.

Dykstra vs. Bagel Boss.