We present a census of the population of deeply embedded young stellar objects (YSOs) in the Perseus molecular cloud complex based on a combination of Spitzer Space Telescope mid-IR data from the c2d legacy team and JCMT/SCUBA submillimeter maps from the COMPLETE team. The mid-IR sources detected at 24 micron and having [3.6]-[4.5] > 1 are located close to the center of the SCUBA cores, typically within 15" of their peaks. The narrowness of the spatial distribution of mid-IR sources around the peaks of the SCUBA cores suggests that no significant dispersal of the newly formed YSOs has occurred. This argues against the suggestion that motions of protostars regulate the time scales over which significant (Bondi-Hoyle) accretion can occur. The most deeply embedded YSOs are found in regions with high extinction, AV > 5, similar to the extinction threshold observed for the SCUBA cores. All the SCUBA cores with high concentrations have embedded YSOs, but not all cores with low concentrations are starless. An unbiased sample of 49 deeply embedded YSOs is constructed. Embedded YSOs are found in 40 of the 72 SCUBA cores with only three cores harboring multiple embedded YSOs within 15". The equal number of SCUBA cores with and without embedded YSOs suggests that the time scale for the evolution through the dense prestellar stages, where the cores are recognized in the submillimeter maps and have central densities of 5e4-1e5 cm^{-3}, is similar to the time scale for the embedded protostellar stages. The current star formation efficiency of cores is estimated to be approximately 10-15%. In contrast, the star formation efficiency averaged over the cloud life time and compared to the total cloud mass is only a few percent, reflecting also the efficiency in assembling cloud material into the dense cores forming stars. ; Comment: Accepted for publication in ApJ (36 pages, 13 figures)