Lenny Simmons says he got a call from the L.A. County Medical Examiner's Office, and they told him, "Richard's death was accidental due to complications from falls and heart disease as a contributing factor" ... according to Simmons family spokesperson Tom Estey.

TMZ confirmed the info with Estey -- lining up with the story we broke last month about Richard's final days. As we reported, he fell in his bathroom the evening of his 76th birthday, and when his housekeeper came to help him up .. he refused medical care.

Following the autopsy in July, the M.E.'s Office deferred an official finding on Richard's death, pending toxicology results.

The Medical Examiner has yet to release its report, but obviously, gave Richard's brother a heads-up.

TMZ broke the story ... Richard was found dead in his home in the Hollywood Hills by his housekeeper on July 13.

First responders were called to the scene, where he was pronounced dead a mere day after his birthday.

Law enforcement sources noted in July that cops initially did not suspect foul play ... and were investigating the death as a natural one.

Richard skyrocketed to fame after launching The Anatomy Asylum -- later renamed Slimmons -- and a series of fitness tapes and DVDs, including "Sweatin' to the Oldies," "Party off the Pounds," "Blast Off," "Pump and Sweat" "Tonin' Uptown," "Tonin' Downtown," etc.

He often portrayed himself in a number of TV appearances, including a 72-episode stint on "General Hospital."

Richard notably took a step back from the limelight in the years leading up to his death ... which we explored in "TMZ Investigates: What Happened to Richard Simmons."