Plants carry genetic material in three separate compartments, the nuclear, mitochondrial, and chloroplast genomes. These genomes interact with each other to various degrees and are subject to shared evolutionary drivers exerted by their host organisms. Although animal mitochondrial and nuclear genomes display linked evolutionary rates, a well-documented phenomenon termed “mito-nuclear covariation”, it is not clear whether the three plant genomes display covarying evolutionary signals on a broad scale. We tested for correlated evolutionary rates between nuclear and organellar genomes using extensive data sets from the major clades of land plants (Embryophyta), including mosses, ferns, gymnosperms, and angiosperms. To examine the evolutionary dynamics in parasitic angiosperms, which are under distinctive selective pressures, we also analysed data sets from mistletoes, broomrapes, sandalwoods, and rafflesias. Evolutionary rates of nuclear and organellar genomes were positively linked in each group of land plants tested, except in the parasitic angiosperms. We also found positive correlations between rates of nonsynonymous and synonymous change. Our results reveal extensive evolutionary rate variation across land plant taxa, particularly in mitochondrial genomes in angiosperms. Overall, we find that nuclear, mitochondrial, and chloroplast genomes in land plants share similar drivers of mutation rates, despite considerable variation in life history, morphology, and genome sizes among clades. Our findings lay the foundation for further exploration of the impact of co-evolutionary interactions on shared evolutionary rates between genomes.