Solomon had already won the National Book Critics Circle Award, and Johnson's book had won the Pulitzer Prize.
The Dayton Literary Peace Prize carries an award of $10,000 and will be presented Nov. 3 in Dayton, Ohio.
This year's runners-up were "Billy Lynn's Long Halftime Walk," by Ben Fountain (also winner of a National Book Critics Circle Award) and "Devil in the Grove," by Gilbert King.
The list of nominees had included Louise Erdrich's novel, "The Round House," winner of a National Book Award and a Minnesota Book Award, and a memoir of Romania, "Burying the Typewriter," published by Graywolf Press.
The peace prize is awarded annually to books that use the power of literature to foster peace and understanding.