The facilities are to be moved from Town Quay to the Eastern Docks to make way for a £450m waterfront development, due to go before planners in August.
Red Funnel plans to build the £35m ferry terminal at the Trafalgar Dock to improve links with the Isle of White.
It will include a four-deck car park above the marshalling yard to replace existing surface parking and car storage
Kevin George, CEO at Red Funnel, said: “We’re delighted that the plans have been approved.
“This is a major step for Red Funnel in terms of delivering the first part of the Solent Gateways scheme alongside the proposals for East Cowes, which are also being progressed.