This paper presents identification of solar coronal mass ejection (CME) sources for 27 major geomagnetic storms (defined by disturbance storm time index ≤ -100 nT) occurring between 1996 and 2000. Observations of CMEs and their solar surface origins are obtained from the Large Angle and Spectrometric Coronagraph (LASCO) and the EUV Imaging Telescope (EIT) instruments on the SOHO spacecraft. Our identification has two steps. The first step is to select candidate front-side halo (FSH) CMEs using a fixed 120 hr time window. The second step is to use solar wind data to provide further constraints, e.g., an adaptive time window defined based on the solar wind speed of the corresponding interplanetary CMEs. We finally find that 16 of the 27 (59%) major geomagnetic storms are identified with unique FSH CMEs. Six of the 27 events (22%) are associated with multiple FSH CMEs. These six events show complex solar wind flows and complex geomagnetic activity, which are probably the result of multiple halo CMEs interacting in interplanetary space. A complex event occurs when multiple FSH CMEs are produced within a short period. Four of the 27 (15%) events are associated with partial-halo gradual CMEs emerging from the east limb. The surface origin of these events is not known because of a lack of any EIT signature. We believe that they are longitudinally extended CMEs having a component moving along the Sun-Earth connection line. One of the 27 major geomagnetic storms is caused by a corotating interaction region. We find an asymmetry in the longitudinal distribution of solar source region for the CMEs responsible for major geomagnetic storms. They are more likely to originate from the western hemisphere than from the eastern hemisphere. In terms of latitude, most geoeffective CMEs originate within a latitude strip of ±30°. The average transit time for a solar CME to arrive at the near-Earth space is found to be 64 hr, while it takes 78 hr on average to reach the peak of the geomagnetic storm. There is a correlation between CME transit time from the Sun to the near-Earth space (T, in hours) and the CME initial velocity (V, in unit of kilometers per second) at the Sun, which can be simply described as T = 96 - (V/21). We also find that while these geoeffective CMEs are either full-halo CMEs (67%) or partial-halo CMEs (30%), there is no preference for them to be fast CMEs or to be associated with major flares and erupting filaments.