We consider the propagation of gravitational waves (GWs) in de Sitter spacetime and how a non-zero value of the cosmological constant might affect their detection in pulsar timing arrays (PTAs). If Λ ≠ 0, the waves are anharmonic in Friedmann-Robertson-Walker coordinates, and although this effect is very small it gives rise to noticeable consequences for GWs originating in extragalactic sources such as spiraling black hole binaries. The results indicate that the timing residuals induced by GWs from such sources in PTAs will show a peculiar angular dependence with a marked enhancement around a particular value of the angle subtended by the source and the pulsars, depending mainly on the actual value of the cosmological constant and the distance to the source. The position of the peak could represent a gauge of the value of Λ. The enhancement that the new effect brings about could facilitate the first direct detection of GWs while representing a local measurement of Λ.