Gluten-free baked products (GFBPs) usually present unbalanced nutritional and unappealing organoleptic characteristics (e.g. excessive hardness and pale color) when compared to cereal-based products containing gluten. Jerusalem artichoke tubers store inulin and fructooligosaccharides, compounds with nutritional and functional attributes suitable for the diets of persons with diabetes and obesity. This work proposes to improve the nutritional and organoleptic characteristics of GFBPs formulated from a base gluten-free premix of maize and cassava starch, and rice flour, by partial substitution (0–70%) of both starches with Jerusalem artichoke flour (JAF). JAF proximate composition and technofunctional properties were evaluated, standing out its high water retention capacity (3.30 ± 0.21 g/g), which was 2 and 3 times higher than that of rice flour and corn and cassava starches, respectively. Firstly, a sweep of replacement percentages for cassava and corn starches with JAF was conducted. The GFBPs formulations assayed were: rice flour (30%), cassava starch (0–30%), maize starch (0–40%), and JAF (0–70%). From color and texture results, the formulations containing 20 (T20) and 40% (T40) of substitution were selected and scaled up, and the respective GFBPs were characterized by moisture content, aw, color, weight, volume, alveolar distribution, and crumb and crust texture properties. The luminosity (L*) of the dough and crust decreased significantly (p < 0.05) with increasing JAF content (from 88.10 ± 0.96 to 44.31 ± 0.74 and from 81.19 ± 1.59 to 35.25 ± 1.50, respectively). Hardness was significantly reduced (p < 0.05) by JAF replacement in T40 compared to the control, from 4.68 ± 1.60 to 1.71 ± 0.34 N for the crumb and from 31.67 ± 9.81 to 3.00 ± 3.31 N for the crust. The T20 samples presented greater alveolar area and circularity of the alveoli, resulting in a GFBP with better textural and organoleptic attributes. Both formulations were acceptable when subjected to a sensory analysis, but consumers showed greater preference for the samples with 40% JAF.