The new coronavirus disease 2019 (COVID-19) has required the implementation of severe mobility restrictions and social distancing measures worldwide. While these measures have been proven effective in abating the epidemic in several countries, it is important to estimate the effectiveness of testing and tracing strategies to avoid a potential second wave of the COVID-19 epidemic. We integrate highly detailed (anonymized, privacy-enhanced) mobility data from mobile devices, with census and demographic data to build a detailed agent-based model to describe the transmission dynamics of SARS-CoV-2 in the Boston metropolitan area. We find that enforcing strict social distancing followed by a policy based on a robust level of testing, contact-tracing and household quarantine, could keep the disease at a level that does not exceed the capacity of the health care system. Assuming the identification of 50% of the symptomatic infections, and the tracing of 40% of their contacts and households, which corresponds to about 9% of individuals quarantined, the ensuing reduction in transmission allows the reopening of economic activities while attaining a manageable impact on the health care system. Our results show that a response system based on enhanced testing and contact tracing can play a major role in relaxing social distancing interventions in the absence of herd immunity against SARS-CoV-2.