The tunnel, which is being built by Musk's Boring Company, will contain autonomous electric skates capable of transporting cars and people at speeds of up to 125-150mph.
A bank of elevators would take pedestrians, cyclists or cars from street-level stations to underground tunnel stops.
Musk said on Twitter that the Boring Company will hold an opening event to showcase the test tunnel on the night of December 10. In June he said the fare would be $1 per passenger.
Ryanair passenger reported to police after racist rant at elderly woman
He yells: "I tell you what, I hope someone sits there because I don't want to sit next to your ugly face, your ugly f****** face". David Lawrence , who filmed what happened, told BBC Radio 5 Live: "Everything was calm, we were getting ready to take off".
The Boring Company initially started off as a joke on Twitter while Musk was stuck in a traffic jam in Los Angeles.
According to The Boring Company website, the Hawthorne tunnel "leaves SpaceX property (parking lot east of Crenshaw Boulevard and south of 120th Street), turns west under 120th Street, and remains under 120th Street for up to 2-miles".
The company is also working on other projects including a Dugout Loop in Los Angeles to transport baseball fans directly to Dodger Stadium, and an express service from O'Hare airport to downtown Chicago.
The Boring Company also aims to enable ultra high-speed transit through the use of pod-and-tube transportation systems, known as a Hyperloop. Companies developing the technology include Virgin Hyperloop One and Hyperloop Transportation Technologies.