The current study systematically analyzes the impact of solidity (σ) and number of blades (n) on the aerodynamic performance of 2-, 3- and 4-bladed Darrieus H-type vertical axis wind turbines (VAWTs). Solidity varies within the wide range of 0.09–0.36. A large number of operational parameters, i.e., tip speed ratio (λ), Reynolds number (Re), turbulence intensity and reduced frequency (K) are investigated to provide a deeper insight into the impact of σ and n on the dynamic loads on blades, the turbine performance and the wake. High-fidelity unsteady Reynolds-averaged Navier-Stokes (URANS) simulations, extensively validated with experiments, are employed. The results show that the turbine optimal tip speed ratio (λopt) is invariant to a newly-introduced parameter ‘σλ3’, regardless of the turbine geometrical and operational characteristics. In addition, a new correlation is derived to estimate λopt as a function of σ, which can also be employed to predict the optimal σ for a turbine with a given λ. It is also found that: (i) for constant-speed urban VAWTs, which due to the low mean wind speed in the urban environment, frequently operate at moderate to high λ, a relatively-low σ is optimal; (ii) an optimal VAWT is a moderately-high-solidity variable-speed rotor maintaining a relatively-low λ, where due to the large blade chord length the resulting Re and K are favorably high; (iii) within the turbine optimal operational range, turbine power coefficient (CP) is almost independent of n. The present findings support the optimal aerodynamic design of small-to large-scale VAWTs. •New insights on the impact of solidity σ and number of blades for VAWTs.•A new correlation for optimal tip speed ratio λopt and σ.•λopt is found to be invariant to ‘σλ3’ for different conditions.•In the optimal regime, power coefficient is almost independent of number of blades.•Reduced frequency is shown as a critical parameter on turbine power performance.