Milk fat plays an important role in the texture of yogurt. Thus, producing fat-free yogurt is a challenge for the food industry. We investigated and modeled the effect of yogurt composition and process parameters on the texture properties obtained by analyzing the texture profile analysis (TPA) and on the rheological properties. The experiment followed the Box-Behnken (DBB) design with three factors: centrifuge rotational speed (CRS) (3000, 4250 and 5500 rpm), casein (Cas) (3.4, 4.9 and 6.4% p/v) and transglutaminase enzyme (TgE) (0, 1 and 2 U/g of protein) concentrations. A complete second-order model better explained the effect of factors on texture properties. Desirability function was selected for the optimization of responses (firmness, cohesiveness and apparent viscosity placed at a maximum level and adhesiveness, gumminess, thixotropy and loss tangent (tan δ) were placed at a minimum level). The results suggest that the addition of TgE showed less effect on texture properties. The optimized values of each factor, Cas, TgE and CRS were, respectively, 3.4%, 1 U/g of protein and 5500 rpm with general desirability (D) of 0.6531. Under these conditions, it is possible to prepare a concentrated fat-free yogurt with a higher protein content due to the concentration, obtained after centrifugation, as well as obtaining desirable texture characteristics such as greater firmness and consistency, low gumminess and adhesiveness.