Spontaneous reactivation of brain activity from learning to a subsequent off-line period has been implicated as a neural mechanism underlying memory consolidation. However, similarities in brain activity may also emerge as a result of individual, trait-like characteristics. Here, we introduced a novel approach for analyzing continuous electroencephalography (EEG) data to investigate learning-induced changes as well as trait-like characteristics in brain activity underlying memory consolidation. Thirty-one healthy young adults performed a learning task, and their performance was retested after a short (∼1 h) delay. Consolidation of two distinct types of information (serial-order and probability) embedded in the task were tested to reveal similarities in functional networks that uniquely predict the changes in the respective memory performance. EEG was recorded during learning and pre- and post-learning rest periods. To investigate brain activity associated with consolidation, we quantified similarities in EEG functional connectivity between learning and pre-learning rest (baseline similarity) and learning and post-learning rest (post-learning similarity). While comparable patterns of these two could indicate trait-like similarities, changes from baseline to post-learning similarity could indicate learning-induced changes, possibly spontaneous reactivation. Higher learning-induced changes in alpha frequency connectivity (8.5–9.5 Hz) were associated with better consolidation of serial-order information, particularly for long-range connections across central and parietal sites. The consolidation of probability information was associated with learning-induced changes in delta frequency connectivity (2.5–3 Hz) specifically for more local, short-range connections. Furthermore, there was a substantial overlap between the baseline and post-learning similarities and their associations with consolidation performance, suggesting robust (trait-like) differences in functional connectivity networks underlying memory processes.