"You are loved and cherished, dearly, forever," she told the doctor, a father of two with movie star looks. "You have nothing to fear. There is nothing you can do wrong."
Alexander recounts his story, and seeks to explain it, in "Proof of Heaven: A Neurosurgeon's Journey into the Afterlife," to be published in the United States on October 23.
His New York publisher failed to respond to interview requests, but an excerpt from "Proof of Heaven" in Newsweek magazine has stirred the enduring debate about life after death.
Inevitably, skeptics wonder if Alexander, who teaches at Harvard Medical School, is going out on a paranormal limb.
"It sounds like he had nothing more than an intense lucid dream," wrote one reader on Newsweek's website. "A personal anecdote is not evidence or proof, as moving as it may be," added another.
The sarcastic New York blog Gawker challenged its readers to spot the difference, if any, between Alexander's portrayal of paradise with published accounts of LSD trips.
But others stood firmly by Alexander, who has previously spoken of his near-death experience on science TV programs and in a lengthy interview last year with Skeptico.com, a science and spirituality blog.