Short answer: Yes, masks are effective if worn properly and hands are kept properly sanitized. Widespread masking also prevents asymptomatic people from spreading the virus. Masks have the ancillary benefit of showing solidarity, reducing stigma, and showing a willingness to follow health guidelines.
Longer answer: Since the COVID-19 is such a new virus, there hasn’t been enough time to conduct extensive studies on its capacity for replication, transmission, and survivability. However, there have been many studies on the use of face masks for other viruses like influenza, rhinoviruses, and other coronaviruses. These studies have found that face masks are quite effective at reducing the spread of infectious respiratory droplets, which is the primary way COVID-19 spreads. According to the CDC, COVID-19 is capable of being spread by asymptomatic carriers, which means that people who feel healthy could be spreading it. This makes masking even more important for preventing the spread of COVID-19. While masks do offer some protection from contracting the virus yourself, the primary use of a mask is to prevent asymptomatic and symptomatic people from spreading the virus through the population. Countries that experienced the Sars outbreak in 2003 have been far more effective at preventing the spread of COVID-19 partially because mask wearing became part of the culture. With everyone wearing some degree of protection, it makes it much harder for the virus to keep finding hosts.