Long-term memory depends on memory consolidation that seems to rely on learning-induced changes in the brain activity. Here, we introduced a novel approach analyzing continuous EEG data to study learning-induced changes as well as trait-like characteristics in brain activity underlying consolidation. Thirty-one healthy young adults performed a learning task and their performance was retested after a short (~1h) delay, that enabled us to investigate the consolidation of serial-order and probability information simultaneously. EEG was recorded during a pre- and post-learning rest period and during learning. To investigate the brain activity associated with consolidation performance, we quantified similarities in EEG functional connectivity of learning and pre-learning rest (baseline similarity) as well as learning and post-learning rest (post-learning similarity). While comparable patterns of these two could indicate trait-like similarities, changes in similarity from baseline to post-learning could indicate learning-induced changes, possibly spontaneous reactivation. Individuals with higher learning-induced changes in alpha frequency connectivity (8.5-9.5 Hz) showed better consolidation of serial-order information. This effect was stronger for more distant channels, highlighting the role of long-range centro-parietal networks underlying the consolidation of serial-order information. The consolidation of probability information was associated with learning-induced changes in delta frequency connectivity (2.5-3 Hz) and seemed to be dependent on more local, short-range connections. Beyond these associations with learning-induced changes, we also found substantial overlap between the baseline and post-learning similarity and their associations with consolidation performance, indicating that stable (trait-like) differences in functional connectivity networks may also be crucial for memory consolidation.