Three-dimensional (3D) hydrogel structures are finding use in fundamental studies of self-assembly, rheology, and 3D cell culture. Most techniques for 3D hydrogel formation are 'single pot', in which gels are not addressable after formation. For many applications, it would be useful to be able to form arrays of gels bearing mixtures of constituents and/or formed from composites of different gel materials. Here, in response to this challenge, we introduce a digital microfluidic method for 'on-demand' formation of arrays of microgels bearing arbitrary contents and shapes. On formation of the gels, each microgel is individually addressable for reagent delivery and analysis. We demonstrate the utility of the method for 3D cell culture and higher-order tissue formation by implementing the first sub-microlitre recapitulation of 3D kidney epithelialization. We anticipate this platform will enable new research that can exploit the flexible nature of this technique for forming and addressing arrays of hydrogels with unique geometries and contents.