At first, the trains will run from downtown to the La Cienega/Jefferson station, a distance of 8.5 miles. This summer, the route will be extended another mile to Culver City.
It's the first rail service to the Westside in 50 years. The cars are expected to carry 22,000 passengers a day.
Officials hope the train will give relief to those weary of driving on the parallel Interstate 10 Freeway.
The $932-million project, which connects with the existing Red, Blue and Purple lines, was begun in 2006 and had been expected to open last year.
The $1.5-billion second stage extending the train to Santa Monica is expected to be running by 2016.
The Associated Press contributed to this report.