Several solutes (e.g., growth factors, cationic solutes, etc.) can reversibly bind to the extracellular matrix (ECM) of biological tissues. Binding interactions have significant implications on transport of such solutes through the ECM. In order to fully delineate transport phenomena in biological tissues, knowledge of binding kinetics is crucial. In this study, a new method for the simultaneous determination of solute anisotropic diffusivity and binding reaction rates was presented. The new technique was solely based on Fourier analysis of fluorescence recovery after photobleaching (FRAP) images. Computer-simulated FRAP tests were used to assess the sensitivity and the robustness of the method to experimental parameters, such as anisotropic solute diffusivity and rates of binding reaction. The new method was applied to the determination of diffusivity and binding rates of 5-dodecanoylaminofluorescein (DAF) in bovine coccygeal annulus fibrosus (AF). Our findings indicate that DAF reversibly binds to the ECM of AF. In addition, it was found that DAF diffusion in AF is anisotropic. The results were in agreement with those reported in previous studies. This study provides a new tool for the simultaneous determination of solute anisotropic diffusion tensor and rates of binding reaction that can be used to investigate diffusive-reactive transport in biological tissues and tissue engineered constructs.