Wheat bran offers health benefits as a baking ingredient, but is detrimental to bread textural quality. Dextran production by microbial fermentation improves sourdough bread volume and freshness, but extensive acid production during fermentation may negate this effect. Enzymatic production of dextran in wheat bran was tested to determine if dextran-containing bran could be used in baking without disrupting bread texture. The Weissella confusa VTT E-90392 dextransucrase gene was sequenced and His-tagged dextransucrase Wc392-rDSR was produced in Lactococcus lactis. Purified enzyme was characterized using 14C-sucrose radioisotope and reducing value-based assays, the former yielding Km and Vmax values of 14.7 mM and 8.2 µmol/(mg·min), respectively, at the pH optimum of 5.4. The structure and size of in vitro dextran product was similar to dextran produced in vivo. Dextran (8.1% dry weight) was produced in wheat bran in 6 h using Wc392-rDSR. Bran with and without dextran was used in wheat baking at 20% supplementation level. Dextran presence improved bread softness and neutralized bran-induced volume loss, clearly demonstrating the potential of using dextransucrases in bran bioprocessing for use in baking.