Wheat bran is an agro-industrial by-product having huge potential for value-added utilisation in biorefinery processes. In this study, a two-step, dilute-sulphuric-acid fractionation process was developed to gain xylose-rich and arabinose-enriched hydrolysates separately. In the first step the reaction time and acid concentration were optimised by statistical evaluation. Depending on the parameters of the optimisation, two process conditions resulting in high arabinose (62–74%) but low xylose yields (41–45%) were determined. Arabinose biopurification of the obtained hydrolysates by Ogataea zsoltii resulted in pure arabinose solutions (arabinose purity of 91–94%). The second acidic hydrolysis resulted in xylose-rich hydrolysates containing 20 g/L xylose. The effect of pH and aeration on the xylitol fermentation by Ogataea zsoltii was investigated. Xylitol fermentation on the xylose-rich hydrolysate under the best conditions resulted in a xylitol yield of 53% in the bioreactor. Hence, an integrated process for arabinose and xylitol production from wheat bran was invented.