The coroner's office on Thursday identified the man as 23-year-old James Llamas. He has previous arrests for drugs and robbery, police said.
The fall came after Llamas had been on top of the crane hundreds of feet in the air, dancing, rolling around and at one point removing his clothes.
After the hours-long standoff and bizarre behavior, Llamas fell from the crane. He died at the scene.
The chase started around 3:50 p.m. in the area of Mid-City by the westbound 91 Freeway. Authorities began a chase with the suspect, who they believed had stolen a white SUV.
At some point, authorities lost the vehicle on the 91 Freeway. He was spotted again around 5:40 p.m. and headed through Carson on the 405 Freeway.
The chase eventually ended up in Long Beach and then in the Wilmington area along the waterfront. Llamas was able to easily blow through two guardhouses at the port with no barriers or other obstructions in his way.
After driving around erratically for several minutes, Llamas fled from the car, leaving it to roll away.
Los Angeles City Councilman Joe Buscaino, who called for a full investigation into the incident, said Llamas could have been carrying anything in the vehicle that entered into the region's most sensitive zone for commerce.
The Port of Los Angeles processes $750 million worth of goods per day.
Port officials said in a statement that Los Angeles Port Police have launched an investigation into the security breach at the container terminal that led to Llamas being able to climb the crane.
"This thorough review, including protocols necessary to address improvements, will be completed as soon as possible," port officials said.
The suspect, donning a Los Angeles Lakers Kobe Bryant jersey, climbed up several flights of stairs before breaking into a room through a window on the door and then quickly hopping back out.
The man was last seen wandering around the top of the crane-like structure, hundreds of feet above the ground.
Later in the evening, the suspect removed all of his clothing and did acrobatic movements on the 3-foot wide beam.
At one point, it appeared the man was going to fall as he tried shimmying over a support beam, but he was able to grab onto some nearby wires and pull himself over to the edge of a beam.
SWAT crisis negotiators arrived to the scene and tried to talk to the man, who again began doing acrobatic movements on the thin wires surrounding the beam.
Police say the SWAT officers were not near the man when he fell. It is not immediately known if he slipped or jumped, police said.