The former "Food Network" star's official cause of death is an allergic reaction resulting in anaphylactic shock, leading to a heart attack ... the coroner in Napa County tells TMZ.

We're told Michael's allergic reaction sent him to a hospital, where he was brought back to life only to later die of hypoxic-ischemic encephalopathy -- a brain dysfunction caused by a lack of oxygen and blood flow.

The coroner also tells us recent cocaine use was another "significant condition" noted in the final findings on Chiarello's death ... but we're told although cocaine was in his system, he did NOT die from a drug overdose.

As we reported ... Michael died Oct. 7 at Queen of the Valley Medical Center in Napa, where he was hospitalized due to an allergic reaction.

It's still unclear if Michael's fatal allergic reaction was food-related, or what it stemmed from.

Michael had a long run on TV, with his show "Easy Entertaining With Michael Chiarello" airing for 10 seasons on Food Network.

The star chef was also featured on hit series like "Chopped," "The Next Iron Chef" and "Top Chef."