The jury said his book was a "clear winner", despite it being a strong year for theatre biographies.
The actor beat five others including books by fellow actor Michael Pennington and the late West Side Story playwright Arthur Laurents.
The other shortlisted titles were Sweet William and The Rest of the Story, by Pennington and Laurents respectively; Charles Dickens and The Great Theatre of The World by Simon Callow; Strindberg, A Life by Sue Prideaux; and In Two Minds: A Biography of Jonathan Miller by Kate Bassett.
Everett's first memoir, Red Carpets and Other Banana Skins, became an international bestseller following its publication in 2006.
In Vanished Years he reveals more stories from his childhood as well as tragic and comic encounters involving both friends and rivals.
Chaired by Morley's widow Ruth Leon, this year's panel included theatre critic Mark Shenton, director Braham Murray and the actor and writer Isla Blair, who was on last year's shortlist for A Tiger's Wedding.
The jury said Everett's book - "a first-hand account of the everyday life of a working and highly successful actor from the inside" - was "just plain fun to read."
The prize, presented in memory of the late critic and writer Sheridan Morley, honours a biography, autobiography or diary in theatre or showbusiness published in the preceding calendar year.
Morley, who wrote 37 books during his lifetime, specialised in biographies of actors, directors and theatre and film personalities.