The ß-type Ti-42Nb alloy was processed by laser powder bed fusion (LPBF) with an infrared top hat laser configuration aiming to control the Young's modulus by creating an adapted crystallographic texture. Utilizing a top hat laser, a microstructure with a strong 〈0 0 1〉 texture parallel to the building direction and highly elongated grains was generated. This microstructure results in a strong anisotropy of the Young's modulus that was modeled based on the single crystal elastic tensor and the experimental texture data. Tensile tests along selected loading directions were conducted to study the mechanical anisotropy and showed a good correlation with the modeled data. A Young's modulus as low as 44 GPa was measured parallel to the building direction, which corresponds to a significant reduction of over 30% compared to the Young's modulus of the Gaussian reference samples (67–69 GPa). At the same time a high 0.2% yield strength of 674 MPa was retained. The results reveal the high potential of LPBF processing utilizing a top hat laser configuration to fabricate patient-specific implants with an adapted low Young's modulus along the main loading direction and a tailored mechanical biofunctionality.