The video, which also captured the signal-caller saying "Are we going to jail or not?", was made available on TMZ's YouTube page:
The incident occurred in Austin, Texas, and TMZ Sports noted Young's blood alcohol content was later measured at three times the legal limit.
The release of the video comes after agent Leigh Steinberg announced Young's intention to return to football on his Twitter page Wednesday. Steinberg also said he and Young "opened discussions" with the CFL's Saskatchewan Roughriders.
Young is still probably best known for his days as a dual-threat quarterback for the Texas Longhorns. He led his team to a thrilling 41-38 victory over USC at the Rose Bowl to capture the 2005 season's national title.
The Tennessee Titans picked him with the No. 3 overall pick in the ensuing draft, and he won the Associated Press Offensive Rookie of the Year and made two Pro Bowls. However, he struggled as a member of the Philadelphia Eagles in 2011 with four touchdowns and nine interceptions in six games and hasn't appeared in a regular-season game since.
Max Olson of ESPN.com noted the Green Bay Packers cut him in 2013, and the Cleveland Browns did the same in 2014.
According to Olson, Young was sentenced to 18 months probation and was fined $300 following the DWI charge. He also had to complete 60 hours of community service.