Relation of decadal variations of the North Atlantic Oscillation index (NAOI) to the 11-year solar cycle in the sunspot number is analyzed for almost 200-year observational period with the use of cross-spectral and cross-wavelet techniques. Based on wavelet transforms of a pair of time series, local cross characteristics such as the local coherency and local correlation are used to study time evolution of the solar–NAOI relationship. The analysis of the NAOI is supplemented and confirmed by similar analysis of more than 300-year long data of Central England temperature (CET). Both the solar cycle–NAOI and solar cycle–CET relationships exhibit a quasi-periodic oscillation with the mean period of about 50 years, which includes a subinterval with positive coherency and a subinterval with negative coherency between the solar cycle and the 11-year modes of the NAOI and CET. The same multidecadal modulation of the solar–NAOI relationship is manifested in the temporal structure of the local correlation between the 11-year modes of the NAOI and the sunspot number at specific time lags of the NAOI relative to the sunspot number. It is distinct in the local correlations for the extended winter period (November–March) NAOI lagging by 7 years after the sunspot number. At this lag, the NAOI anticorrelates in general with the sunspot number and the local anticorrelation reinforces periodically with the aforementioned ∼50 year period. At the 1-year lag, which differs from the 7-year lag by a half solar cycle, the 11-year mode of the winter NAOI correlates in general with the solar cycle but the correlation is mainly associated with the last 70-year time interval. The change in the sign of the solar–NAOI relationship is also the case for the extended summer periods of the year (May–September). For this period, the approximately mirror image of the local correlations is observed at the 7-year and 1-year lags. The multidecadal modulation is likely associated with periods of enhanced solar impact on the NAO.