The 14-cap Italy international was found dead in his hotel room at the weekend ahead of La Viola's league meeting with Udinese.
Astori's cause of death was initially unknown, leading to an autopsy being ordered to discover whether a manslaughter case could be called.
Any wrongdoing has now officially been ruled out following preliminary tests, however, with a slow resting heart rate being given as the most probable cause.
Antonio De Nicolo, the chief prosecutor of Udine, told Italian outlet RAI: "Based on the evidence of the autopsy examination, carried out on March 6, 2018, on the body of Davide Astori, with reference to the cause of death, this cause can be indicated as of a cardiac nature, most likely a bradyarrhythmia with pluri-visceral congestion and a pulmonary oedema.
"For a definite diagnosis, more profound histological examinations are necessary. From the preliminary results, it does not seem like there is any external causes other than that of a natural death, but prudently our advisers are telling us that we must wait for the result of histological examinations before making a definitive statement.
"They have asked for 60 days to complete their report and that is when we will have a complete overview."
Astori's body will be transported to Florence on Wednesday, a day before the late defender's funeral is held.