In this paper, we study long-term changes in the main directions of movement (storm tracks) of extratropical cyclones in the North Atlantic over the period 1873–2021. It was found that in the cold half of the year (the period of the most intense cyclogenesis), the average latitudes of storm tracks in the longitudinal range from 60° to 10° W experience oscillations with periods ∼80–100, ∼40–47, and ∼22 years, indicating their possible association with solar activity variations. The trajectories of cyclones were shifted to the north at the minimum of the Gleissberg secular cycle (∼1900–1930) and to the south at the cycle maximum (∼1940–1960). The secular changes in storm track latitudes amount to ∼3°–5° in the western part of the North Atlantic (the area of formation and the most intensive development of cyclones). On the bidecadal scale, a northward shift of cyclone trajectories in even solar cycles and a southward shift in odd ones were found. The shift of cyclone trajectories to the north in even cycles reached maximal values (∼1°–2° relative to a secular variation) at the descending branch and the minimum of the solar cycle (2nd−6th years after the maximum) in the eastern part of the North Atlantic. Changes in intensity of the stratospheric polar vortex, caused by variations in galactic cosmic rays and geomagnetic activity, are a possible reason for oscillations in cyclone trajectories.