Maria has headed probes into 1993 Mumbai blasts and 26/11 attacks on the city.
The decision to appoint Maria, currently the chief of Maharashtra Police's Anti-Terrorism squad, was taken after a high-level meeting here chaired by Chief Minister Prithviraj Chavan and attended by Home Minister R R Patil.
Maria, a 1981 batch IPS officer, headed the probe into the 1993 Mumbai blasts.
Singh was the first serving Mumbai Police chief to resign. He was due to retire in 2015.