Tuberculosis (TB) diagnosis in regions with limited resources depends on microscopy with insufficient sensitivity. Rapid diagnostic tests of low cost but high sensitivity and specificity are needed for better point-of-care management of TB. Trained African giant pouched rats (Cricetomys sp.) can diagnose pulmonary TB in sputum but the relevant Mycobacterium tuberculosis (Mtb)-specific volatile compounds remain unknown. We investigated the odour volatiles of Mtb detected by rats in reference Mtb, nontuberculous mycobacteria, Nocardia sp., Streptomyces sp., Rhodococcus sp., and other respiratory tract microorganisms spiked into Mtb-negative sputum. Thirteen compounds were specific to Mtb and 13 were shared with other microorganisms. Rats discriminated a blend of Mtb-specific volatiles from individual, and blends of shared, compounds (P = 0.001). The rats’ sensitivity for typical TB-positive sputa was 99.15% with 92.23% specificity and 93.14% accuracy. These findings underline the potential of trained Cricetomys rats for rapid TB diagnosis in resource-limited settings, particularly in Africa where Cricetomys rats occur widely and the burden of TB is high.