An effective medium model is developed for disordered metamaterials containing a spatially random distribution of dielectric spheres. Similar to effective medium models for ordered metamaterials, this model predicts resonances in the effective permeability and permittivity arising from electricand magnetic-dipole Mie resonances in the spheres. In addition, the model predicts a redshift of the electric resonance with increasing particle loading. Interestingly, when the particle loading exceeds the percolation threshold of 33%, the model predicts that the electric resonance overlaps with the magnetic resonance, resulting in a negative refractive index.Metamaterials, inhomogeneous composite materials that behave macroscopically as homogeneous materials, are of great fundamental and technological interest. The ability to tailor the macroscopic electromagnetic parameters, namely the permittivity and permeability, by changing the geometry and arrangement of the included elements has led to a number of important material designs and applications [1]. Most notable among these are materials with negative refractive index [2,3], which have both negative permittivity and permeability. Negative index materials exhibit unusual properties such as negative refraction and exponential growth of evanescent near fields, which have been utilized for applications such as cloaking [4] and superresolution imaging [5].To date, the metamaterial literature has focused primarily on designs where the included elements are arranged in a periodic lattice [6]. This is largely due to the ease of computation and suppression of scattering, as disorder of the lattice leads to spatial inhomogeneities. However, fabrication of periodic metamaterials on a large scale can be cost prohibitive, particularly for metamaterials operating in the optical band, where the lattice dimensions are submicron and require the use of electronbeam lithography [7,8]. Self-assembly based nanosphere lithography has been used to fabricate centimeter-scale optical metasurfaces [9], but this approach is not scalable to much larger areas.Disordered metamaterials provide a scalable alternative to periodic structures, provided that the scattering can be managed and their performance can be predicted. However, relatively few works have focused on disordered metamaterials. These limited studies have shown that size [10-13] and positional [14-23] disorder of a metamaterial's resonator elements lead to resonance broadening and effective scattering loss. While these works provide important insights, they overlook one of the most important aspects of disorder: percolation. Percolation occurs in random composites at high loading when the particles form a continuous path through the composite, and it can have dramatic consequences on the effective electromagnetic parameters [24,25] In this Letter, it is shown that percolation induces a negative refractive index in disordered metamaterials containing Mie-resonant particles. To this end, the classic Bruggeman percolation theory [24,26] ...