Motorists will be charged $2.44 for a one-way journey on the 4-kilometre stretch of the first stage of the motorway by 2025, but will end up paying more as they will have no choice but to connect to the WestConnex toll road.
The new stage one tunnels, being constructed by CIMIC Groups CPB Contractors and UGL, is slated to save motorists 15 minutes between Kogarah and the Anzac Bridge, as well as 12 minutes from Mascot to Taren Point.
The motorway was previously known as the F6 extension, with a corridor reserved for the road since the 1950s.
Mr Constance said the 4 kilometre tunnels would bypass 23 sets of traffic lights and reduce traffic on General Homes Drive by about 10,000 vehicles per day.
Seven commercial properties and four homes will be acquired as part of the build.
Mr Constance said he expected an improved process for any future acquisitions as the transport department conducts an internal review into the practice following a damning Auditor-Generals report last week.
Opposition roads spokesman John Graham said the government was focusing too much on toll roads and not enough on public transport.
Without plans for public transport or stage two this is more about toll revenue than a transport solution, Mr Graham said.
That community concern has deepened after the minister was unwilling today to spell out the plans for stage two.