A new method solely based on spatial Fourier analysis (SFA) was developed to completely determine a two-dimensional (2D) anisotropic diffusion tensor in fibrous tissues using fluorescence recovery after photobleaching (FRAP). The accuracy and robustness of this method was validated using computer-simulated FRAP experiments. This method was applied to determine the region-dependent anisotropic diffusion tensor in porcine temporomandibular joint (TMJ) discs. The average characteristic diffusivity of 4 kDa FITC-Dextran across the disc was 26.05 ± 4.32 μm²/s which is about 16% of its diffusivity in water. In the anteroposterior direction, the anterior region (30.99 ± 5.93 μm²/s) had significantly higher characteristic diffusivity than the intermediate region (20.49 ± 5.38 μm²/s) and posterior region (20.97 ± 2.46 μm²/s). The ratio of the two principal diffusivities represents the anisotropy of the diffusion and ranged between 0.45 and 0.51 (1.0 = isotropic). Our results indicated that the solute diffusion in TMJ discs is inhomogeneous and anisotropic. These findings suggested that diffusive transport in the TMJ disc is dependent on tissue composition (e.g., water content) and structure (e.g., collagen orientation). This study provides a new method to quantitatively investigate the relationship between solute transport properties and tissue composition and structure.