DNA origami has proven useful for organizing diverse nanoscale components into patterns with 6 nm resolution. However for many applications, such as nanoelectronics, large-scale organization of origami into periodic lattices is desired. Here, we report the self-assembly of DNA origami rectangles into two-dimensional lattices based on stepwise control of surface diffusion, implemented by changing the concentrations of cations on the surface. Previous studies of DNA–mica binding identified the fractional surface density of divalent cations (ñ(s2))as the parameter which best explains the behaviour of linear DNA on mica. We show that for ñ(s2) between 0.04 and 0.1, over 90% of DNA rectangles were incorporated into lattices and that, compared with other functions of cation concentration, ñ(s2) best captures the behaviour of DNA rectangles. This work shows how a physical understanding of DNA–mica binding can be used to guide studies of the higher-order assembly of DNA nanostructures, towards creating large-scale arrays of nanodevices for technology.