Free water fraction (FWF) represents the amount of water per unit volume of brain parenchyma, which is not bound to macromolecules. Its excess in multiple sclerosis (MS) is related to increased tissue loss. The use of mcDESPOT (multicomponent driven single pulse observation of T1 and T2), a 3D imaging method which exploits both the T1 and T2 contrasts, allows FWF to be derived in clinically feasible times. However, this method has not been used to quantify changes of FWF and their potential clinical impact in MS. The aim of this study is to investigate the changes in FWF in MS patients and their relationship with tissue damage and cognition, under the hypothesis that FWF is a proxy of clinically meaningful tissue loss. To this aim, we tested the relationship between FWF, MS lesion burden and information processing speed, evaluated via the Symbol Digit Modalities Test (SDMT). In addition to standard sequences, used for T1‐ and T2‐weighted lesion delineation, the mcDESPOT sequence with 1.7 mm isotropic resolution and a diffusion weighted imaging protocol (b = 0, 1200 s/mm2, 40 diffusion directions) were employed at 3 T. The fractional anisotropy map derived from diffusion data was used to define a subject‐specific white matter (WM) atlas. Brain parenchyma segmentation returned masks of gray matter (GM) and WM, and normal‐appearing WM (NAWM), in addition to the T1 and T2 lesion masks (T1L and T2L, respectively). Ninety‐nine relapsing–remitting MS patients (age = 43.3 ± 9.9 years, disease duration 12.3 ± 7.7 years) were studied, together with twenty‐five healthy controls (HC, age = 38.8 ± 11.0 years). FWF was higher in GM and NAWM of MS patients, compared to GM and WM of HC (both p < .001). In MS patients, FWF was the highest in the T1L and GM, followed by T2L and NAWM, respectively. FWF increased significantly with T1L and T2L volume (ρ ranging from 0.40 to 0.58, p < .001). FWF in T2L was strongly related to both T1L volume and the volume ratio T1L/T2L (ρ = 0.73, p < .001). MS patients performed worse than HC in the processing speed test (mean ± SD: 54.1 ± 10.3 for MS, 63.8 ± 10.8 for HC). FWF in GM, T2L, perilesional tissue and NAWM increased with SDMT score reduction (ρ = −0.30, −0.29, −0.33 respectively and r = −.30 for T2L, all with p < .005). A regional analysis, conducted to determine which NAWM regions were of particular importance to explain the relationship between FWF and cognitive impairment, revealed that FWF spatial variance was negatively related to SDMT score in the corpus callosum and the superior longitudinal fasciculus, WM structures known to be associated with cognitive impairment, in addition to the left corticospinal tract, the sagittal stratum, the right anterior limb of internal capsule. In conclusion, we found excess free water in brain parenchyma of MS patients, an alteration that involved not only MS lesions, but also the GM and NAWM, impinging on brain function and negatively associated with cognitive processing speed. We suggest that the FWF metric, derived from noninvasive, rapid MRI acquisitions and bearing good biological interpretability, may prove valuable as an MRI biomarker of tissue damage and associated cognitive impairment in MS.