Sydney's multibillion-dollar CBD light rail will open to the public on December 14 after months of delay.

The light rail, which will carry passengers between Circular Quay and Randwick, will be free to the public for its opening weekend, according to Premier Gladys Berejiklian.

"The CBD and South East Light Rail is a big step towards revitalising our city and will transform the way we live, work and go out in Sydney," Ms Berejiklian said.

Originally slated to cost $1.6 billion, the light rail project blew out to just under $3 billion following delays and complications with Spanish subcontractor Acciona.