Two-dimensional materials with both ferromagnetism and ferroelasticity present new possibilities for the development of spintronics and multifunctional devices. These materials offer a novel way of controlling the magnetization axis direction by switching the ferroelastic state, enabling efficient and low-power magnetic device operation. Such properties make them promising candidates for the next generation of non-volatile memory, sensors, and logic devices. By performing the first-principles calculations, we systematically investigated the ferromagnetism, ferroelasticity, and magnetoelastic coupling in MoTeX (X=F, Cl, Br, I) monolayers. The results indicate that MoTeX monolayers are intrinsic semiconductors holding both ferromagnetism and ferroelasticity. The pronounced in-plane magnetic anisotropy suggests that MoTeX monolayers can resist thermal disturbances and maintain long-range magnetic order. The Curie temperatures of MoTeX monolayers are 144.75, 194.55, 111.45, and 92.02 K, respectively. Our calculations show that the four MoTeX monolayers possess two stable ferroelastic states, with their easy magnetization axes perpendicular to each other. The ferroelastic transition barriers between the two ferroelastic states of MoTeF, MoTeCl, MoTeBr, MoTeI monolayers are 0.180, 0.200, 0.209, and 0.226 eV/atom, respectively, with reversible strains of 54.58%, 46.32%, 43.06%, and 38.12%. These values indicate the potential for reversible magnetic control through reversible ferroelastic transitions at room temperature. Owing to their unique magnetoelastic coupling properties, MoTeX monolayers demonstrate the ability of control on reversible magnetization axis at room temperature, laying the foundation for the development of highly controllable and stable spintronic devices.