A low-cost method of manufacturing a composite tube assembly having a composite fiber tube connected to metallic end fittings includes placing at least one end fitting on a mandrel, the end fitting including a grip region having a plurality of external surfaces, wrapping a fiber tow around the grip region of each end fitting and the mandrel to form a fiber-wrapped assembly, curing the fiber tow, and removing the mandrel to yield a completed tube assembly. The method may include positioning a plurality of compression inserts around the grip region after some of the fiber tow has been wrapped around the grip region, and wrapping additional fiber tow around the compression inserts and the grip region. The compression inserts may have a rounded outer surface such that an end portion of the tube wound around the compression inserts has a round outer cross-sectional shape.