Magnetic flux noise is a dominant source of dephasing and energy relaxation in superconducting qubits. The noise power spectral density varies with frequency as $1/f^{\alpha }$, with $\alpha \lesssim 1$, and spans 13 orders of magnitude. Recent work indicates that the noise is from unpaired magnetic defects on the surfaces of the superconducting devices. Here, we demonstrate that adsorbed molecular ${\mathrm{O}}_2$ is the dominant contributor to magnetism in superconducting thin films. We show that this magnetism can be reduced by appropriate surface treatment or improvement in the sample vacuum environment. We observe a suppression of static spin susceptibility by more than an order of magnitude and a suppression of $1/f$ magnetic flux noise power spectral density of up to a factor of 5. These advances open the door to the realization of superconducting qubits with improved quantum coherence.