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Metric perturbations induced by ultralight dark matter (ULDM) fields havelong been identified as a potential target for pulsar timing array (PTA)observations. Previous works have focused on the coherent oscillation of metricperturbations at the characteristic frequency set by the ULDM mass. In thiswork, we show that ULDM fields source low-frequency stochastic metricfluctuations and that these low-frequency fluctuations can produce distinctivedetectable signals in PTA data. Using the NANOGrav 12.5-year data set andsynthetic data sets mimicking present and future PTA capabilities, we show thatthe current and future PTA observations provide the strongest probe of ULDMdensity within the solar system for masses in the range of $10^{-18}\;{\rmeV}-10^{-16}\;{\rm eV}$.

Stochastic Ultralight Dark Matter Fluctuations in Pulsar Timing Arrays