VERDICT (vascular, extracellular and restricted diffusion for cytometry in tumours) estimates and maps microstructural features of cancerous tissue non-invasively using diffusion MRI. The main purpose of this study is to address the high computational time of microstructural model fitting for prostate diagnosis, while retaining utility in terms of tumour conspicuity and repeatability. In this work, we adapt the accelerated microstructure imaging via convex optimization (AMICO) framework to linearize the estimation of VERDICT parameters for the prostate gland. We compare the original non-linear fitting of VERDICT with the linear fitting, quantifying accuracy with synthetic data, and computational time and reliability (performance and precision) in eight patients. We also assess the repeatability (scan-rescan) of the parameters. Comparison of the original VERDICT fitting versus VERDICT-AMICO showed that the linearized fitting (1) is more accurate in simulation for a signal-to-noise ratio of 20 dB; (2) reduces the processing time by three orders of magnitude, from 6.55 seconds/voxel to 1.78 milliseconds/voxel; (3) estimates parameters more precisely; (4) produces similar parametric maps and (5) produces similar estimated parameters with a high Pearson correlation between implementations, r ²  > 0.7. The VERDICT-AMICO estimates also show high levels of repeatability. Finally, we demonstrate that VERDICT-AMICO can estimate an extra diffusivity parameter without losing tumour conspicuity and retains the fitting advantages. VERDICT-AMICO provides microstructural maps for prostate cancer characterization in seconds.