TMZ obtained Connery's death cert and it shows he died from respiratory failure as a result of pneumonia, old age and atrial fibrillation ... an irregular heart rate that can increase the risk of strokes, heart failure and other heart-related complications.

The doc shows he died on October 31 at 1:30 AM at his home in the Bahamas. His occupation is listed as a retired actor. As we reported ... Sean's wife, Micheline Roquebrune, said Sean died peacefully in his sleep. He was 90.

Sean, of course, became a huge star in 1962 after "Dr. No" was released. He went on to star in 7 Bond films between 1962 and 1983 -- "From Russia with Love," "Goldfinger," "Thunderball," "You Only Live Twice," "Diamonds are Forever," and "Never Say Never Again."

He also starred in "The Hunt for Red October," "Indiana Jones and the Last Crusade" and "The Rock."