Background: Accelerated brain atrophy is a main determinant of the progressing disabilities clinically characterizing people with multiple sclerosis (MS). Preliminary data from animal studies and human phase 1 studies indicate a possible disease-modifying effect of physical exercise. We therefore assessed whether high-intensity progressive aerobic exercise (PAE) affects brain atrophy in MS. Methods: We conducted a 24-week randomized, controlled, cross-over, phase 2 trial, including an exercise group (24 weeks of supervised PAE followed by self-guided physical activity) and a waitlist group (24 weeks of habitual lifestyle followed by supervised PAE). Participants were recruited at four Danish hospitals. MS patients aged 18-65 years with an Expanded Disability Status Scale score of 0-6 willing to travel to the trial and training facility were randomly assigned (1:1) by the sealed envelope principle, stratified by sex. The primary outcome was percentage brain volume change (PBVC) after 24 weeks, analyzed using an intention-to-treat linear mixed effects model. Findings: A total of 86 participants were recruited from 28 April 2016 to 10 October 2017 (43 patients were assigned to each group). PBVC was -0·29% (SD 0·63) in the exercise group; -0·17% (0·99) in the placebo group (between-group change +0·12%, 95% CI -0·27-0·51; p=0·545). We observed higher grey matter parenchymal fraction (+1·13 percentage points, 0·00-2·26; p=0·05) and cardiorespiratory fitness (+3·5 mL O2/min/kg, 2·0-5·1; p<0·0001) and lower annualized relapse rate (p=0·0023) in the exercise group. No serious adverse events were observed. Interpretation: These findings do not support a ‘whole brain’ neuroprotective effect of PAE (i.e. total brain atrophy) in people with MS. Oppositely, improved cardiorespiratory fitness was accompanied by a ‘regional brain’ neuroprotective effect (i.e. grey matter parenchymal fraction) and a relapse rate of zero. These findings justify recommending PAE as a possible adjunct disease-modifying treatment in MS and warrant further long-term, large-scale phase 3 investigations. Trial Registration Number: ClinicalTrials.gov identifier: NCT02661555. Funding Statement: Jascha Fonden, Fonden for Neurologisk Forskning, The Danish Multiple Sclerosis Society, Aase og Ejnar Danielsens Fond, Knud og Edith Eriksens Fond, Augustinus Foundation, Direktor Emil C. Hertz og Hustru Inger Hertz’ Fond, Else og Mogens Wedell-Wedellsborgs Fond, and Karen A. Tolstrups Fond. Declaration of Interests: ML-C has received teaching honoraria from Novartis. UD has received research support, travel grants, and/or teaching honoraria from Biogen Inc., Merck Serono, Novartis, and Sanofi. LGH has received research support, travel grant, and/or teaching honoraria from Biogen Inc. and Sanofi. TP has received research support from Biogen Inc., Merck, Roche, Alexion, Sanofi, and Novartis. No other authors have any disclosures. Ethics Approval Statement: Ethics approval was obtained from the ethical committee of the Central Denmark Region, Denmark (record no. 1-10-72-291-15).