Ongoing neural activity unfolds over intrinsic timescales that vary widely across the brain. The increase in timescales along the sensory-transmodal cortical axis parallels the cortical hierarchy, while diversity of timescales within each area may reflect functional specialization of individual neurons. However, mechanisms that give rise to the diversity of timescales within and across brain areas remain largely unknown. We leveraged a brain-wide dataset of single-neuron activity to characterize the intrinsic timescales across the whole mouse brain. Timescales varied widely across brain regions, with the midbrain and hindbrain exhibiting five-fold slower timescales on average than the forebrain. Despite the large variation in timescales across areas, their distribution within each area followed a universal power law with a consistent scaling exponent of p ~ - 2, spanning the range of tens of milliseconds to several seconds. To understand mechanisms that may generate this universal scaling of timescales, we studied recurrent neural network models with random connectivity across a range of parameters controlling the connectivity distribution and dynamical regimes. We found that the power-law distribution of timescales emerges in networks with heavy-tailed connectivity operating in a chaotic regime, which occurs when the synaptic gain parameter is sufficiently large. In the chaotic regime, the exponent of the timescale distribution follows that of the connectivity distribution independent of the synaptic gain, while the median timescale depends on both the synaptic gain and connectivity exponent. The scaling exponent of p ~ - 2 matches the previously reported exponent in connectome data, supporting the correspondence between connectivity and timescale distributions suggested by our models. Our findings reveal the organizing principles of timescale variation throughout the entire mouse brain and propose a unifying network mechanism for the emergence of diverse timescales across the brain and their universal scaling within each area.