Organic waste streams, otherwise known as organic amendments (OA), contain potentially valuable nutrients which may additionally increase legacy nutrient availability in soil. This is particularly the case for phosphorus (P) where declining reserves of rock phosphate add an extra dimension to their utility. In acidic soils, OA have been reported to increase P availability through the action of O-aryl and carbonyl groups (represent organic acid compounds) by substituting previously fixed, legacy P and forming organometallic complexes to reduce P sorption. This study aimed to investigate if signature P (orthophosphate) and C (O-aryl and carbonyl) content of OA could be used to predict soil P availability, to replace traditional ways of testing OA and also for future prescriptive applications. Food waste and biosolid were the sources of OA in this study, with pyrolysis and composting processes used to create a range of functional groups. Nuclear magnetic resonance (NMR) spectroscopy was utilized to identify forms of C (solid-state 13C NMR) and P compounds (solution-state 31P NMR) in these OA. The O-aryl, carbonyl, and orthophosphate content were higher in pyrolysis and composted materials compared to their feedstock substrate. The effect of OA addition on soil P availability was monitored in a 110-day laboratory incubation study. Results showed an increase in soil P availability (Olsen P) and a decrease in soil P buffering capacity (PBC) after incubation. The increase in soil P availability was not predicted well by the NMR-derived orthophosphate content of OA, which may be due to the overestimation of plant-available orthophosphate content by the solution-state 31P NMR. Furthermore, an additional increase in soil ΔOlsen P (difference between observed and expected) was obtained above the Olsen P added from OA indicating substitution of previously fixed soil P. Both indices of P availability namely ΔOlsen P (r = 0.63–0.83) and ΔPBC (difference between treatment—control) (r = −0.50 to −0.80) showed strong (but opposite) correlations with the ratio of O-aryl to carbonyl C content of OA. It was concluded that the ratio of O-aryl and carbonyl C content of OA could be used to predict the P availability in acidic soil.