K-Pax series by Gene Brewer (Books 1 & 2)

K-Pax (K-Pax #1)
Psychiatrist Gene Brewer doesn't have a diagnosis for the mysterious new patient who calls himself "prot" (rhymes with goat). But this strange and likeable man cannot be--as he claims--from the planet K-PAX.
Or can he? Prot knows facts about space that are confounding the experts. He is soon revealing Dr. Brewer's own deepest pains and most sublime longings. And his tales of K-PAX have other patients competing to go along with him when he heads "home". Now the doctor is racing the clock to find prot's true identity before he losses a man whose "madness" might just save them all. . .

On a Beam of Light (K-Pax #2)
Five years to the day, almost to the second, after he disappeared form the Manhattan Psychiatric Institute, leaving his host body in a catatonic state, the being known as prot (rhymes with goat) has returned. Now, in sixteen more sessions with psychiatrist Gene Brewer, prot reveals that he has come back to escort a chosen few to his home planet, K-PAX.
K-PAX is an idyllic planet free of the pain and suffering of earth. Prot has incredible insights into how to cure that suffering, and his radical ideas have made him a celebrity. Now, legions of people are longing to follow him home.
But Dr. Brewer has heard it before. Five years ago, he discovered another person buried deep in prot's personality: Robert Porter of Montana. The mystery of Robert's illness and of prot's true origins lie deep within Robert's shattered psyche. Now Dr. Brewer must race against the clock to unlock the secrets of Robert's traumatic past and not only save his patient but maybe humanity.