Crystalline two-dimensional (2D) semiconductors often combine high elasticity and in-plane strength, making them ideal for strain-induced tuning of electronic characteristics, akin to strategies used in silicon electronics. However, existing techniques have not achieved strain in 2D materials that is simultaneously high in magnitude (>1%), stable over long periods, and spatially and directionally programmable. In this context, programmable strain means that the strain level and direction can be deterministically engineered across a single layer. Here, we apply spatially programmable biaxial strain (e_b) up to ~2.2% with a spatial gradient of ~0.1 %e_b um-1 in monolayer MoS2 via conformal transfer onto patterned substrates fabricated using two-photon lithography. The induced e_b is stable for months and enables local band gap tuning of ~0.4 eV in monolayer MoS2, ~25% of its intrinsic band gap. Further, by tailoring substrate topography, we introduce uniaxial (anisotropic) strain, demonstrating control over both strain magnitude and direction. We also extend this strain engineering framework to MoS2-WS2 bilayer heterostructures. Overall, we introduce a distinct regime of strain-enabled control in 2D semiconductors to support the development of optoelectronics and nanoelectronics with engineered optical and electronic landscapes.