There are two features that need to be distinguish here: one is the Hudson Submarine Canyon on the continental slope, which starts at around 100 m and connects to the deep basin; and the Hudson Shelf Valley on the continental shelf, which is much shallower (20-100m).
Assuming the question is about the Shelf Valley, Butman et al. (2003) provided a thorough explanation of the origin and features of the valley. Here is their discussion:
The 150-km-long Hudson Shelf Valley, the largest physiographic feature on the mid-Atlantic continental shelf, bisects the New York Bight region (sheet 1 figure 1, and sheet 2, figure 6 and figure 7). The Valley is the submerged seaward extension of the ancestral Hudson River drainage system that, unlike other valleys on the Atlantic shelf, has not been filled with sediment. The valley head is located in a broad shallow basin (Christiansen Basin) and extends offshore 5-40 m below the shelf surface to a seaward terminus at a shelf-edge delta (Ewing and others, 1963; Emery and Uchupi, 1972; Uchupi and others, 2001).
The ancestral Hudson River is hypothesized to have begun to develop in the Late Cretaceous when post-Atlantic rifting caused continued uplift and tilting of the margin, resulting in landward erosion and marginal seaward growth that continued into the Tertiary (Weiss, 1974). The Hudson Shelf Valley is thought to have been repeatedly downcut during periods of Pleistocene marine regression (Suter and others, 1949; Weiss, 1974). This downcutting possibly was amplified by the proposed catastrophic drainage of late Wisconsinan glacial lakes 12,000 - 14,000 yr BP (Newman and others, 1969; Uchupi and others, 2001). At this time, the shoreline was located approximately at the 60 m isobath (Thieler and others, 1999). At 12,000 - 14,000 yr BP, the large glacial lakes north of the New York Bight are thought to have breached the moraine front at the Verrazano Narrows and other locations in New Jersey and New York (Newman and others, 1969; Soren, 1971; Lovegreen, 1974). Boring data at the Verrazano Narrows indicate that more than 100 m of Pleistocene and Cretaceous sedimentary material was eroded as a result of this breaching event(s), along with most of the lacustrine sediment deposited during the previous 8,000 yr (Newman and others, 1969). Uchupi and others (2001) propose that late Wisconsin erosion of the Hudson Shelf Valley and deposition of sediment lobes (figure 1) on the outer shelf were a consequence of this catastrophic drainage.