Invasions of introduced species have homogenized ecological communities worldwide, leading to losses of native species and the services they provide. Some of these invaders substantially alter nutrient cycling, which changes conditions for all other organisms, but less is known about the potential influence of these species on nitrogen (N) trace gas emissions that affect atmospheric processes. We used a natural experiment to explore whether the establishment of an introduced nitrogen (N) fixing tree (Falcataria moluccana) and recent invasion of an amphibian predator, the Caribbean tree frog (Eleutherodactylus coqui), into native Hawaiian rainforests has affected soil emissions of nitrous oxide (N2O) and nitric oxide (NO), two atmospherically important trace gases produced by soil microorganisms. Soil N2O and NO emissions and rates of soil N cycling were significantly higher in F. moluccana-dominated stands compared to native Metrosideros polymorpha (Ohi’a) stands. Additionally, invasion of E. coqui frogs moderately increased soil N2O emissions, primarily in non-native F. moluccana forests where soil N availability was already elevated. N2O emissions were positively and significantly related to net potential N mineralization, and total N2O+NO fluxes increased with soil nitrate (NO3-) concentration and rates of nitrification. Previous work in these Hawaiian rainforest sites has shown that F. moluccana substantially increases N availability by increasing ecosystem N supply compared to uninvaded stands, and E. coqui accelerates N availability and litter decomposition, although moderately, due to enhanced fluxes of nutrient-rich waste products. Here, we show that acceleration of nutrient cycling by introduced species can also alter biosphere-atmosphere exchange of N-oxides.