On the third attempt, he managed to pull the drawstring loop tight around the reptile - despite its efforts to free itself by thrashing from side to side.
Officer Vargas then placed his jacket over the animal's head to calm it down, and used his bare hands to clamp its huge jaws shut before a colleague bound its mouth shut with a strap.
Sharing the video on their Facebook page, Boynton Beach Police Department said: "A few weeks ago, Officer Alfredo Vargas responded to a call from a resident of Hunter's Run who found an alligator laying by his front door.
"He learned how to handle/wrestle alligators at the Native Village in Hollywood, Florida. Officer Vargas called the Florida Fish and Wildlife Conservation Commission and learned that it would be about 30 minutes before a trapper could arrive, and it was likely that the trapper would kill the alligator.
"Officer Vargas said he didn't want that to happen given his background with learning how to capture nuisance gators and return them to their natural habitat."
The Florida Fish and Wildlife Conservation Commission told Officer Vargas he was allowed to released the reptile wherever he liked, so according to the police department he put the alligator in the back seat of his patrol car and set it free in a nearby canal.
Boynton Beach Police Department added: "Officer Vargas removed the tape from around its mouth and put him back in the water. Officer Vargas doesn't know it yet, but we've just made him the department's official alligator wrestler (kidding but not really)."