Recent epidemics of Zika virus (ZIKV) in the Pacific and the Americas have highlighted its potential as an emerging pathogen of global importance. ZIKV is a member of the family Flaviviridae, genus Flavivirus, and is transmitted to humans by Aedes mosquito species. Both Ae. aegypti and Ae. albopictus are known to transmit ZIKV. However, variable vector competence has been observed between mosquito populations from different geographical regions. Australia remains at risk of ZIKV introduction due to its close proximity to the Western Pacific, the presence of susceptible mosquito vectors in Northern Queensland, and favorable environmental conditions. Therefore, we evaluated the vector competence of Ae. aegypti from Queensland and Ae. albopictus from the Torres Strait Islands, for a Brazilian epidemic strain of ZIKV. Mosquitoes were exposed to an infectious blood meal, and reared at either constant or fluctuating temperatures (mean of 28°C). Virus RNA copies in mosquito bodies, distal tissues (wings and legs) and saliva were quantified post infection. Overall, both species supported high viral body titers (>107 copies/mosquito body) at 14 days post infection (dpi), with no significant differences in viral copy number between constant and cyclic temperature regimes. Infection rates at 14 dpi were similar for both species. Despite high infection rates in both vectors, the transmission rates of ZIKV to saliva in Ae. aegypti (60%) was significantly higher than in Ae. albopictus (10%) at 14 dpi. A significant difference in viral copy number in wings and legs between species was observed, with higher titers in Ae. aegypti. Exposure to constant versus fluctuating temperature also had a significant effect on viral titer in Ae. aegypti. Our results are in agreement with the role of Ae. aegypti in the global emergence of ZIKV, and suggest that Ae. aegypti are more competent for transmission of ZIKV than Ae. albopictus. Therefore, Ae. aegypti is likely to be the primary potential vector of ZIKV in Australia, which should be taken into account during disease risk evaluation.