Much attention is recently paid to the global warming observed in the 20th century, and especially to the relative impact of natural and anthropogenic factors responsible for it. Many studies have revealed a good correlation, up to the last decades, between century-scale changes in global surface temperature and solar activity, though the mechanism is still controversial. Long-term anomalies of atmospheric parameters are often connected to large-scale changes in atmospheric circulation influencing, through teleconnections, distant and apparently unconnected areas. Such large-scale phenomena are El Nino/Southern Oscillation (ENSO) and North Atlantic Oscillation (NAO) affecting the climate over a great part of the globe on interannual to decadal and centennial time-scales. Little is known about the factors determining the long-term variability of these phenomena. In the present paper we compare the century-long variability of NAO and ENSO with the solar activity variations in the secular (Gleissberg) solar cycle and find a close relation between them. We suggest that the influence of solar activity on these large-scale phenomena is mediated by atmospheric centers of action which undergo changes in intensity and location in response to long-term variations of solar activity.