Abstract Non‐native species have invaded most parts of the world, and the invasion process is expected to continue and accelerate. Because many invading non‐native species are likely to become permanent inhabitants, future consideration of species‐area relationships (SARs) should account for non‐native species, either separately or jointly with native species. If non‐native species occupy unused niches and space in invaded areas and extinction rate of native species remains low (especially for plants), the resultant SARs (with both native and non‐native species) will likely be stronger. We used published and newly compiled data (35 data sets worldwide) to examine how species invasions affect SARs across selected taxonomic groups and diverse ecosystems around the world. We first examined the SARs for native, non‐native, and all species. We then investigated with linear regression analyses and paired or unpaired t tests how degree of invasion (proportion of non‐native species) affected postinvasion SARs. Postinvasion SARs for all species (native plus non‐native) became significantly stronger as degree of invasion increased ( r 2 = 0.31, p = 0.0006), thus, reshaping SARs worldwide. Overall, native species still showed stronger and less variable SARs. Also, slopes for native species were steeper than for non‐native species (0.298 vs. 0.153). There were some differences among non‐native taxonomic groups in filling new niches (especially for birds) and between islands and mainland ecosystems. We also found evidence that invasions may increase equilibrial diversity. Study of such changing species–area curves may help determine the probability of future invasions and have practical implications for conservation.