Exclusive Details

Tiger Woods was asleep at the wheel in a stopped car at 2:03 AM -- about 8 miles from his house -- when cops came upon him before his arrest, and he was completely out of it.

According to the police report, obtained by TMZ Sports, Woods was in his 2015 Mercedes asleep at the wheel with the motor running and right blinker flashing. The report says Woods "had extremely slow and slurred speech."

He told cops he was "coming from L.A. California from golfing." He then changed his story and said he didn't know where he was.

According to the report, 4 drugs were listed under medical conditions -- Solarex, Vicodin, Torix and Vioxx. It notes Vioxx was not taken this year. It says Tiger had 4 left knee surgeries and 4 Achilles.

The report says he flunked the field sobriety test badly ... he couldn't do the one-leg stand or the nose touch. The report says when asked if he understood the Romberg alphabet test, he stated, "yes, recite entire national anthem backwards."

According to the report, Woods was arrested and taken to a testing facility. At 4:28 AM, he took a breathalyzer test and blew zeros. It says he was "cooperative as much as possible, very droopy, extremely sleepy, hard to keep eyes open, hard to walk."

Tiger has since said he had an "unexpected reaction to prescribed medications" ... adding, "I didn't realize the mix of medications affected me so strongly."