The project is a key enabling scheme for the £1bn–£1.5bn New QEH development, which received government funding confirmation in April.
The car park will be built in two phases, with the first providing 500 spaces and the second adding 879 more, replacing the existing surface parking.
Construction is scheduled to begin in early 2026, with completion by the end of 2027.
R G Carter has been working with QEH since 2019 on various fast-track projects, including RAAC plank replacements and ward refurbishments.
The new car park will be built on the site of the demolished Inspire Centre, which was cleared in June 2023 to make way for the development.
The New QEH programme is expected to move into the next stage of delivery, with work on the new hospital scheduled to begin in 2027–2028.
The new hospital project’s design team includes BDP leading as architect, WSP as structural and civil engineer, and Mott MacDonald handling mechanical, electrical, and public health engineering.