Electron spins in silicon offer a competitive, scalable quantum‐computing platform with excellent single‐qubit properties. However, the two‐qubit gate fidelities achieved so far have fallen short of the 99% threshold required for large‐scale error‐corrected quantum computing architectures. In the past few years, there has been a growing realization that the critical obstacle in meeting this threshold in semiconductor qubits is charge noise arising from the qubit environment. In this work, a notably low level of charge noise of S0 = 0.0088 ± 0.0004 μeV2 Hz−1 is demonstrated using atom qubits in crystalline silicon, achieved by separating the qubits from surfaces and interface states. The charge noise is measured using both a single electron transistor and an exchange‐coupled qubit pair that collectively provide a consistent charge noise spectrum over four frequency decades, with the noise level S0 being an order of magnitude lower than previously reported. Low‐frequency detuning noise, set by the total measurement time, is shown to be the dominant dephasing source of two‐qubit exchange oscillations. With recent advances in fast (≈μs) single‐shot readout, it is shown that by reducing the total measurement time to ≈1 s, 99.99% two‐qubit 𝑆𝑊𝐴𝑃⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√SWAP gate fidelities can be achieved in single‐crystal atom qubits in silicon.