EXCLUSIVE

The two L.A. Dodgers security guards who donned masks and stole a ton of gear from the team clubhouse have finally been punished ... and are officially banned from the memorabilia biz.

We broke the story ... Fernando Sierra and Juan Dedios Prada were caught on video in 2015 sneaking around Dodgers Stadium (in masks) in an effort to steal game-used bats, gloves, etc.

Officials believe the guys had been doing it for a while -- and made serious profits moving the stolen loot with the help of a 3rd man who sold it on eBay.

Now, we've learned the 2 security guards (who have since been fired) cut a deal in which they pled no contest to burglary and got 3 years formal probation.

As part of the deal, they are not allowed to sell any kind of sports memorabilia.

The stakes are high because they also got a 16 month suspended prison sentence -- meaning if they screw up, they go to the slammer.