Anaerobic soil disinfestation (ASD) is considered a promising sustainable alternative to chemical soil fumigation (CSF), and has been shown to be effective against soilborne diseases, plant-parasitic nematodes, and weeds in several crop production systems. Nevertheless, limited information is available on the effects of ASD on crop yield and quality. Therefore, a field study was conducted on fresh-market tomato (Solanum lycopersicum L.) in two different locations in Florida (Immokalee and Citra), to evaluate and compare the ASD and CSF performances on weed and nematodes control, and on fruit yield and quality. In Immokalee, Pic-Clor 60 (1,3-dichloropropene + chloropicrin) was used as the CSF, whereas in Citra, the CSF was Paldin™ [dimethyl disulfide (DMDS) + chloropicrin]. Anaerobic soil disinfestation treatments were applied using a mix of composted poultry litter (CPL) at the rate of 22 Mg·ha−1, and two rates of molasses [13.9 (ASD1) and 27.7 m3·ha−1 (ASD2)] as a carbon (C) source. In both locations, soil subjected to ASD reached highly anaerobic conditions, and cumulative soil anaerobiosis was 167% and 116% higher in ASD2 plots than in ASD1 plots, in Immokalee and Citra, respectively. In Immokalee, the CSF provided the most significant weed control, but ASD treatments also suppressed weeds enough to prevent an impact on yield. In Citra, all treatments, including the CSF, provided poor weed control relative to the Immokalee site. In both locations, the application of ASD provided a level of root-knot nematode (Meloidogyne sp.) control equivalent to, or more effective than the CSF. In Immokalee, ASD2 and ASD1 plots provided 26.7% and 19.7% higher total marketable yield as compared with CSF plots, respectively. However, in Citra, total marketable yield was unaffected by soil treatments. Tomato fruit quality parameters were not influenced by soil treatments, except for fruit firmness in Immokalee, which was significantly higher in fruits from ASD treatments than in those from CSF soil. Fruit mineral content was similar or higher in ASD plots as compared with CSF. In fresh-market tomato, ASD applied using a mixture of CPL and molasses may be a sustainable alternative to CSF for maintaining or even improving marketable yield and fruit quality.