Police say the incident began with a minor crash between two cars about 11.50pm on Friday in the city-bound lanes of the bridge near the Pyrmont exit.
The drivers of the two vehicles - a Toyota Camry sedan and a Holden Captiva station wagon - were standing on the roadway and were allegedly struck by a Holden Commodore sedan, with a taxi also becoming involved.
Authorities said the woman driving the Camry, aged 25 from Sydney, and the man driving the Captiva, aged 38 from Sydney's southwest, died at the scene.
The two were exchanging details in the wake of the initially minor collision, NSW Police Superintendent Robert Toynton suggested.
A man who drove the Commodore has been hospitalised for injuries sustained in the crash as well as mandatory testing.
A man who drove the taxi was taken to hospital for mandatory testing.
Police will investigate whether speed, alcohol or drugs were factors in the crash, and will also look at whether they can obtain any vision from the taxi, Supt Toynton said.
Investigators will also consider where the two people were standing.
"This is an absolute tragic incident of road trauma and absolutely tragic for the families of those people that are now going to be grieving the loss of family members this close to Christmas," Supt Toynton said.
All lanes on the Anzac Bridge had reopened by Saturday morning.
Investigators are urging anyone with dashcam images of the incident to contact them, especially those drivers travelling west-bound between 11.45pm and 11.55pm.
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