Dr Hameroff, Professor Emeritus at the Departments of Anesthesiology and Psychology and Director of the Centre of Consciousness Studies at the University of Arizona, and Sir Roger have been working on the theory since 1996.
They argue that our experience of consciousness is the result of quantum gravity effects inside these microtubules - a process they call orchestrated objective reduction (Orch-OR).
In a near-death experience the microtubules lose their quantum state, but the information within them is not destroyed. Or in layman's terms, the soul does not die but returns to the universe.
Dr Hameroff explained the theory at length in the Morgan Freeman-narrated documentary Through the Wormhole, which was recently aired in the US by the Science Channel.
The quantum soul theory is now trending worldwide, thanks to stories published this week by The Huffington Post and the Daily Mail, which have generated thousands of readers comments and social media shares.
"Let's say the heart stops beating, the blood stops flowing, the microtubules lose their quantum state," Dr Hameroff said.
"The quantum information within the microtubules is not destroyed, it can't be destroyed, it just distributes and dissipates to the universe at large.
'If the patient is resuscitated, revived, this quantum information can go back into the microtubules and the patient says "I had a near death experience".'
In the event of the patient's death, it was "possible that this quantum information can exist outside the body indefinitely - as a soul".
Dr Hameroff believes new findings about the role quantum physics plays in biological processes, such as the navigation of birds, adds weight to the theory.