Electron spin qubits formed by atoms in silicon have large (tens of millielectronvolts) orbital energies and weak spin-orbit coupling, giving rise to isolated electron spin ground states with coherence times of seconds(1,2). High-fidelity (more than 99.9 per cent) coherent control of such qubits has been demonstrated(3), promising an attractive platform for quantum computing. However, inter-qubit coupling-which is essential for realizing large-scale circuits in atom-based qubits-has not yet been achieved. Exchange interactions between electron spins(4,5) promise fast (gigahertz) gate operations with two-qubit gates, as recently demonstrated in gate-defined silicon quantum dots(6-10). However, creating a tunable exchange interaction between two electrons bound to phosphorus atom qubits has not been possible until now. This is because it is difficult to determine the atomic distance required to turn the exchange interaction on and off while aligning the atomic circuitry for high-fidelity, independent spin readout. Here we report a fast (about 800 picoseconds) root SWAP two-qubit exchange gate between phosphorus donor electron spin qubits in silicon using independent single-shot spin readout with a readout fidelity of about 94 per cent on a complete set of basis states. By engineering qubit placement on the atomic scale, we provide a route to the realization and efficient characterization of multi-qubit quantum circuits based on donor qubits in silicon.