A system for mounting an outboard motor propulsion unit to a marine vessel transom includes a support cradle having a head section coupled to a transom bracket and a pair of arms extending aftward from the head section and along opposite port and starboard sides of the propulsion unit. A pair of upper mounts is provided, each upper mount in the pair coupling a respective arm to the propulsion unit aft of a center of gravity of an engine system of the propulsion unit. A pair of lower mounts is also provided, each lower mount in the pair coupling the propulsion unit to the transom bracket. The pair of upper mounts is located aft of the pair of lower mounts when the propulsion unit is in a neutral position, in which the propulsion unit is generally vertically upright and not tilted or trimmed with respect to the transom.