We consider d > 4-dimensional spacetimes which are asymptotically flat at spatial infinity and show that, in the first-order framework, the action principle is well defined without the need of infinite counter-terms. It naturally leads to a covariant phase space in which the Hamiltonians generating asymptotic symmetries provide the total energy–momentum and angular momentum of the isolated system. This work runs parallel to our previous analysis in four dimensions Ashtekar et al (2008 Class. Quantum Grav. 25 095020 (arXiv:0802.2527)). The higher-dimensional analysis is in fact simpler because of the absence of logarithmic and super translation ambiguities.