The cost to taxpayers of Sydney's troubled light rail line has ballooned to at least $2.9 billion - $1.3 billion above the amount first budgeted for the project.

Transport Minister Andrew Constance released the final bill for the project late on Friday, less than two weeks before trams are due to start carrying passengers between Circular Quay and Randwick.

The latest amount represents the third blowout in the expense of one of the Berejiklian government's signature transport projects, originally budgeted at $1.6 billion.

In 2014, the cost of the 12.8-kilometre line to the city's eastern suburbs surged to $2.1 billion due to mispricings and omissions in the business case.