A 2-year field experiment was carried out in a Mediterranean environment to study the effects of vetch (Vicia sativa L.) residue management strategies incorporating green manure (GM) using a roller-crimper (RC) and different organic fertilizers (municipal solid waste compost, anaerobic digestate, and a commercial organic fertilizer) on organic zucchini (Cucurbita pepo L.) yield and quality. Zucchini yield was influenced positively by the vetch residue management strategy, although the response was significantly different between years. The vetch cover crop increased marketable zucchini yield in the first year by 46.6% compared with the fallow (FA) treatment, indicating that this fertility-building crop could reduce off-farm nitrogen (N) fertilizer input for subsequent crops. Averaging over 2 years of the experiment, marketable zucchini yield increased by 15.2% and 38% with the RC mulch and GM plow-down, respectively, compared with the FA treatment, although differences were significant in the first year only. The application of organic fertilizers in vetch management plots increased marketable zucchini yield by 21.8% in the first year compared with the unfertilized control. This result is particularly relevant, because organic fertilizers were applied at ≈50% of the normal application rate for zucchini after taking into account biological N fixation attributable to the vetch. The concentrations of soil mineral N at harvest were 19, 27, and 28 mg·kg−1 for the RC, FA, and GM treatments, respectively. These mineral N concentrations indicated that a portion of applied organic fertilizer N, and N attributable to vetch (GM and RC), remained in the soil at harvest, suggesting the potential for leaching, which should be taken into account in the overall fertilization program. These research findings suggest that effective vetch cover crop management and the application of organic fertilizers can improve yield and quality of organically managed zucchini.