Davoyan was born in Mets Parni, Spitak rayon, Armenian SSR on 3 July 1940.

He published a number of poetry collections (My world, 1963; Massacre of the Crosses, 1972; The sad elephant, 1978).

Davoyan's famous poems include "Unwrap your skin", "The spider", and "After Narekatsi".

Requiem, Massacre of the Crosses, and Toros Rosslin were blocked from publication for a number of years, the latter two eventually being published outside of Armenia.

In 2003, The Little Bird at the Exhibition, a children's book written by Davoyan, was awarded the President's Prize for Literature.