The poem, "Dear Jake," was found in a notebook by producers of the documentary "Philip Larkin and the Third Woman," about his relationship with his former secretary, the BBC reported.
Larkin died in 1985 at the age of 63.
The poem was sent in 1976 to Betty Mackereth, his secretary of 28 years. Mackereth, 87, speaks for the first time about their love affair in the documentary, which marks the 25th anniversary of the poet's death.
Larkin's biographer, Andrew Motion, said finding the poem "Dear Jake" was "a rather amazing and wonderful" find.
The BBC will televise "Philip Larkin and the Third Woman" Sunday.