Age-related white matter hyperintensities are a common feature and are known to be negatively associated with structural integrity, functional connectivity, and cognitive performance. However, this has yet to be fully understood mechanistically. We analyzed multiple MRI modalities acquired in 465 non-demented individuals from the Swedish BioFINDER study including 334 cognitively normal and 131 participants with mild cognitive impairment. White matter hyperintensities were automatically quantified using fluid-attenuated inversion recovery MRI and parameters from diffusion tensor imaging were estimated in major white matter fibre tracts. We calculated fMRI resting state-derived functional connectivity within and between predefined cortical regions structurally linked by the white matter tracts. How change in functional connectivity is affected by white matter lesions and related to cognition (in the form of executive function and processing speed) was explored. We examined the functional changes using a measure of sample entropy. As expected hyperintensities were associated with disrupted structural white matter integrity and were linked to reduced functional interregional lobar connectivity, which was related to decreased processing speed and executive function. Simultaneously, hyperintensities were also associated with increased intraregional functional connectivity, but only within the frontal lobe. This phenomenon was also associated with reduced cognitive performance. The increased connectivity was linked to increased entropy (reduced predictability and increased complexity) of the involved voxels' blood oxygenation level-dependent signal. Our findings expand our previous understanding of the impact of white matter hyperintensities on cognition by indicating novel mechanisms that may be important beyond this particular type of brain lesions.