The £28m project will pave the way for the wider redevelopment of Whipps Cross Hospital with works due to begin on the new hospital in 2025.
Barts Health NHS Trust selected IHP under the ProCure23 Framework.
Work will start in the New Year on the multi-storey car park, which will include chargers for electric vehicles to support the transition to sustainable travel.
Jason Griffiths, Vinci Building’s regional director said: “IHP are delighted to have secured the P23 Whipps Cross car park project for Barts Health NHS Trust.
“The completion of this car park is a major step towards unlocking the future redevelopment”.