The strain-managed optical waveguide assemblies of the present invention utilize a large-mode-area (LMA) optical fiber that is annealed in a first bending such that the fiber in that configuration has substantially no axial strain. A fiber support member is then used to support the annealed LMA optical fiber in a second bending configuration that forms within the LMA optical fiber an axial strain profile that reduces stimulated Brillouin scattering (SBS) as compared to the first bending configuration, and that also preferably causes the LMA optical fiber to operate in a single mode. The LMA optical fiber may have a double-clad configuration and include a doped core that serves as a gain medium. The strain-managed optical waveguide assembly can then be used to constitute a fiber amplifier that mitigates the SBS penalty associated with high-power fiber-based optical systems. The strain-managed waveguide assembly can also provide for thermal management in high-power applications, and can be used to control SBS by controlling the temperature profile along the length of the LMA optical fiber in a manner that mitigates SBS.