Sydney commuters will be able to catch driverless metro trains between Sydney's north west and Chatswood as early as April or May after the first train successfully completed running on the entire length of the 36-kilometre line.

The exact date of the opening of Australia's first driverless passenger line will depend on complex testing of train systems and signalling over the coming weeks, as well as final approval for services by the national safety regulator.

Premier Gladys Berejiklian marks the arrival of the first metro train at Chatswood. Credit:AAP/Jeremy Piper

Premier Gladys Berejiklian doubted people would be fazed by riding on driverless trains, pointing out that they are operating successfully elsewhere in the world such as in Singapore.

"I don't think people will think about it once they are on the system. It will be so efficient, and of course, we will continue to have all of our station staff," she said.