The state government is aiming to have the Sydney Gateway road link in place by the time WestConnex is completed in four years time.
Premier Gladys Berejiklian announced the calling of expressions of interest for the toll-free road from the WestConnex interchange at St Peters to Sydney Airport's domestic and international terminals.
The announcement on Sunday came 36 hours after the opening of the WestConnex M4 tunnels.
Transport Minister Andrew Constance said the aim was for contracts for Sydney Gateway, which is expected to cost $2.2 to $2.6 billion, to be signed mid-2020.
Mr Constance said an environmental impact statement would be released at the end of the year, and it was hoped the project would be completed by 2023 to coincide with the completion of WestConnex.
Sydney Gateway is forecast to take about 10,000 heavy vehicles off streets around the airport and Port Botany.
However, the State Opposition has previously criticised the project for not having a direct connection to Port Botany.
Mr Constance said Sydney Gateway would "improve connections towards Port Botany".
"There will be further time savings from Parramatta, Dee Why, Moorebank and Campbelltown, and relief for Southern Cross Drive, King Georges Road and the M5 East tunnel," he said.
A section of the Port Botany rail freight line is being duplicated as part of the project.
The addition of Sydney Gateway will take the total cost of WestConnex from the original forecast of $10.6 billion to almost $20 billion.